# zbMATH — the first resource for mathematics

## MacMahon, Percy Alexander

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 Author ID: macmahon.percy-alexander Published as: MacMahon; MacMahon, P. A.; MacMahon, P. A. (Major).; MacMahon, Percy A.; MacMahon, Percy Alexander; Macmahon, P. A. External Links: Wikidata · GND · MacTutor
 Documents Indexed: 134 Publications since 1880, including 9 Books Biographic References: 3 Publications
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#### Co-Authors

 128 single-authored 2 Easton, B. S. 2 Knowles, R. L. 2 Mathews, George Ballard 2 Scott, Robert Forsyth 2 Simmons, T. C. 2 Tucker, Robert 1 Ayrton, Herta 1 Barisien, E.-N. 1 Barton, W. J. 1 Beyens, J. 1 Brocard, Henri 1 Busk, E. 1 Chakrvarti, B. 1 Chambeau, A. 1 Curtis 1 Curtis, A. Hill. 1 Darling, H. B. C. 1 Davis, R. F. 1 Gohierre de Longchamps, Gaston Albert 1 Eastwood, D. 1 Galliers, T. 1 Gordon, A. P. L. 1 Greenstreet, William John 1 Hammond, James 1 Hudson, William Henry Hoar 1 Jenkins, J. S. 1 Johnston, J. P. 1 MacFarlane, Alexander 1 MacMahon, W. P. D. 1 Malet, John C. 1 Martin, Artemas 1 McClelland, William J. 1 Mee, W. M. 1 Miller, William John Clarke 1 Morgan, C. Lloyd 1 Mukhopadhyay, Ashutosh 1 Neuberg, Joseph 1 Nilkanta 1 Openshaw, T. W. 1 O’Regan, J. 1 Perrin, E. 1 Rau, B. H. 1 Reeves, J. M. 1 Roberts, Samuel 1 Rutter, E. 1 Scott, Charlotte Angas 1 Symons, E. W. 1 Theodosius, A. F. 1 Townsend, Robert 1 Voyson, W. 1 Young, J. R.
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#### Serials

 15 Proceedings of the London Mathematical Society. Second Series 13 American Journal of Mathematics 13 The Quarterly Journal of Pure and Applied Mathematics 12 Proceedings of the London Mathematical Society 10 Philosophical Transactions of the Royal Society of London, Series A 9 Proceedings of the Cambridge Philosophical Society 5 Nature, London 4 Proceedings of the Royal Society of London. Series A 3 Philosophical Transactions of the Royal Society of London, A 2 Journal of the London Mathematical Society 1 Discrete Applied Mathematics 1 Bulletin de la Société Mathématique de France 1 Comptes Rendus Hebdomadaires des Séances de l’Académie des Sciences, Paris 1 Mathematicians of Our Time 1 The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science, V. Series
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#### Fields

 26 Combinatorics (05-XX) 22 Number theory (11-XX) 4 Linear and multilinear algebra; matrix theory (15-XX) 3 Special functions (33-XX) 3 Ordinary differential equations (34-XX) 2 History and biography (01-XX) 2 Differential geometry (53-XX) 2 Probability theory and stochastic processes (60-XX) 1 General and overarching topics; collections (00-XX) 1 Geometry (51-XX) 1 Mechanics of particles and systems (70-XX) 1 Information and communication theory, circuits (94-XX)

#### Citations contained in zbMATH Open

48 Publications have been cited 883 times in 691 Documents Cited by Year
Combinatory analysis. Vol. 2. JFM 46.0118.07
MacMahon, P. A.
1916
Combinatory analysis. Vol. I, II. Zbl 0101.25102
MacMahon, Percy A.
1960
Combinatory analysis. Vol. 1. JFM 45.1271.01
MacMahon, P. A.
1915
Two applications of general theorems in combinatory analysis: (1) To the theory of inversions of permutations; (2) To the ascertainment of the numbers of terms in the development of a determinant which has amongst its elements an arbitrary number of zero. JFM 46.0107.04
MacMahon, P. A.
1916
The indices of permutations and the derivation therefrom of functions of a single associated with the permutations of any assemblage of objects. JFM 44.0076.02
MacMahon, P. A.
1913
Combinatorial analysis. JFM 31.0219.01
MacMahon, P. A.
1900
Divisors of numbers and their continuations in the theory of partitions. JFM 47.0117.01
MacMahon, P. A.
1920
Memoir on the theory of the compositions of numbers. JFM 25.0258.01
MacMahon, P. A.
1893
Combinatory analysis. Vols. I, II (bound in one volume). Reprint of An introduction to combinatory analysis (1920) and Combinatory analysis. Vol. I, II (1915, 1916). Zbl 1144.05300
MacMahon, Percy A.
2004
Small contribution to combinatory analysis. JFM 46.0108.01
MacMahon, P. A.
1918
Second memoir on the composition of numbers. JFM 39.0241.01
MacMahon, P. A.
1908
Collected papers. Volume I: Combinatorics. Ed. and with a preface by George F. Andrews. With an introduction by Gian-Carlo Rota. Zbl 0557.01015
MacMahon, Percy Alexander
1978
Memoir on the theory of the partitions of numbers. Part V. Partitions in two-dimensional space. JFM 42.0236.21
MacMahon, P. A.
1911
Memoir on the theory of the partition of numbers. – Part IV: On the probability that the successful candidate at an election by ballot may never at any time have fewer votes than the one who is insucessful; on a generalisation of this question, and on its connexion with other questions of partition, permutation, and combination. JFM 40.0281.04
Macmahon, P. A.
1909
Note on the parity of the number which enumerates the partitions of a number. JFM 48.1160.01
MacMahon, P. A.
1921
Memoir on the theory of the partitions of numbers. Part VI. Partitions in two-dimesional space, to which is added an adumbration of the theory of the partitions in three-dimensional space. JFM 42.0237.01
MacMahon, P. A.
1911
Application of a theory of permutations in circular precession to the theory of numbers. JFM 24.0181.01
MacMahon, P. A.
1892
Dirichlet series and the theory of partitions. JFM 50.0083.02
MacMahon, P. A.
1924
The divisors of numbers. JFM 47.0107.02
MacMahon, P. A.
1920
Memoir on the theory of the partition of numbers. Part I. JFM 27.0134.04
MacMahon, P. A.
1896
Partitions of numbers whose graphs possess symmetry. JFM 30.0201.04
MacMahon, P. A.
1899
Memoir on the symmetric functions of the roots of equations. JFM 22.0187.02
MacMahon, P. A.
1890
Combinatory analysis: a review of the present state of knowledge. JFM 28.0103.01
MacMahon, P. A.
1897
Yoke-chains and multipartite compositions in connexion with the analytical forms called “trees”. JFM 23.0132.02
MacMahon, P. A.
1891
Note on the parity of the number which enumerates the partitions of a number. JFM 48.0153.01
MacMahon, P. A.
1921
Seventh memoir on the partition of numbers. JFM 46.0205.03
MacMahon, P. A.
1918
A new method in combinatory analysis, with application to latin squares and associated questions. JFM 30.0227.11
MacMahon, P. A.
1898
Yoke-chains and multipartite compositions in connexion with the analytical forms called trees. JFM 23.0565.02
MacMahon, P. A.
1891
The structure of a determinant. (Lecture on the Rouse Ball Foundation, University of Cambridge, 7. 6. 27.). JFM 53.0074.05
MacMahon, P. A.
1927
Researches in the theory of determinants. JFM 50.0069.01
MacMahon, P. A.
1924
The theory of modular partitions. JFM 48.1161.01
MacMahon, P. A.
1922
The theory of modular partitions. JFM 48.0154.01
MacMahon, P. A.
1922
New mathematical pastimes. JFM 48.0075.06
MacMahon, P. A.
1921
An introduction to combinatory analysis. JFM 47.0066.07
MacMahon, P. A.
1920
Combinations derived from $$m$$ identical sets of $$n$$ different letters and their connexion with general magic squares. JFM 46.0108.02
MacMahon, P. A.
1917
Second memoir on the compositions of numbers. JFM 38.0225.01
MacMahon, P. A.
1907
A second paper on perpetuants. JFM 17.0082.03
MacMahon, P. A.
1885
New mathematical pastimes. With an introduction by Paul Garcia. Reprint of the 1930 2nd impression. Zbl 1154.00010
MacMahon, P. A.
2004
The expansion of determinants and permanents in terms of symmetric functions. JFM 54.0114.03
MacMahon, P. A.
1928
The parity of $$p(n)$$, the number of partitions of $$n$$, when $$n\leqq \, 1000$$. JFM 52.0167.01
MacMahon, P. A.
1926
The sums of powers of the binomial coefficients. JFM 33.0285.05
MacMahon, P. A.
1902
Memoir on the theory of the partitions of numbers. Part. II. JFM 30.0171.11
MacMahon, P. A.
1899
James Joseph Sylvester. JFM 28.0030.03
MacMahon, P. A.
1896
The perpetuant invariants of binary quantics. JFM 26.0141.01
MacMahon, P. A.
1895
A certain class of generating functions in the theory of numbers. JFM 25.0258.02
MacMahon, P. A.
1893
Weighing by a series of weights. JFM 23.0186.03
MacMahon, P. A.
1890
Certain special partitions of numbers. JFM 18.0138.04
MacMahon, P. A.
1886
Seminvariants and symmetric functions. JFM 15.0127.01
MacMahon, P. A.
1883
Combinatory analysis. Vols. I, II (bound in one volume). Reprint of An introduction to combinatory analysis (1920) and Combinatory analysis. Vol. I, II (1915, 1916). Zbl 1144.05300
MacMahon, Percy A.
2004
New mathematical pastimes. With an introduction by Paul Garcia. Reprint of the 1930 2nd impression. Zbl 1154.00010
MacMahon, P. A.
2004
Collected papers. Volume I: Combinatorics. Ed. and with a preface by George F. Andrews. With an introduction by Gian-Carlo Rota. Zbl 0557.01015
MacMahon, Percy Alexander
1978
Combinatory analysis. Vol. I, II. Zbl 0101.25102
MacMahon, Percy A.
1960
The expansion of determinants and permanents in terms of symmetric functions. JFM 54.0114.03
MacMahon, P. A.
1928
The structure of a determinant. (Lecture on the Rouse Ball Foundation, University of Cambridge, 7. 6. 27.). JFM 53.0074.05
MacMahon, P. A.
1927
The parity of $$p(n)$$, the number of partitions of $$n$$, when $$n\leqq \, 1000$$. JFM 52.0167.01
MacMahon, P. A.
1926
Dirichlet series and the theory of partitions. JFM 50.0083.02
MacMahon, P. A.
1924
Researches in the theory of determinants. JFM 50.0069.01
MacMahon, P. A.
1924
The theory of modular partitions. JFM 48.1161.01
MacMahon, P. A.
1922
The theory of modular partitions. JFM 48.0154.01
MacMahon, P. A.
1922
Note on the parity of the number which enumerates the partitions of a number. JFM 48.1160.01
MacMahon, P. A.
1921
Note on the parity of the number which enumerates the partitions of a number. JFM 48.0153.01
MacMahon, P. A.
1921
New mathematical pastimes. JFM 48.0075.06
MacMahon, P. A.
1921
Divisors of numbers and their continuations in the theory of partitions. JFM 47.0117.01
MacMahon, P. A.
1920
The divisors of numbers. JFM 47.0107.02
MacMahon, P. A.
1920
An introduction to combinatory analysis. JFM 47.0066.07
MacMahon, P. A.
1920
Small contribution to combinatory analysis. JFM 46.0108.01
MacMahon, P. A.
1918
Seventh memoir on the partition of numbers. JFM 46.0205.03
MacMahon, P. A.
1918
Combinations derived from $$m$$ identical sets of $$n$$ different letters and their connexion with general magic squares. JFM 46.0108.02
MacMahon, P. A.
1917
Combinatory analysis. Vol. 2. JFM 46.0118.07
MacMahon, P. A.
1916
Two applications of general theorems in combinatory analysis: (1) To the theory of inversions of permutations; (2) To the ascertainment of the numbers of terms in the development of a determinant which has amongst its elements an arbitrary number of zero. JFM 46.0107.04
MacMahon, P. A.
1916
Combinatory analysis. Vol. 1. JFM 45.1271.01
MacMahon, P. A.
1915
The indices of permutations and the derivation therefrom of functions of a single associated with the permutations of any assemblage of objects. JFM 44.0076.02
MacMahon, P. A.
1913
Memoir on the theory of the partitions of numbers. Part V. Partitions in two-dimensional space. JFM 42.0236.21
MacMahon, P. A.
1911
Memoir on the theory of the partitions of numbers. Part VI. Partitions in two-dimesional space, to which is added an adumbration of the theory of the partitions in three-dimensional space. JFM 42.0237.01
MacMahon, P. A.
1911
Memoir on the theory of the partition of numbers. – Part IV: On the probability that the successful candidate at an election by ballot may never at any time have fewer votes than the one who is insucessful; on a generalisation of this question, and on its connexion with other questions of partition, permutation, and combination. JFM 40.0281.04
Macmahon, P. A.
1909
Second memoir on the composition of numbers. JFM 39.0241.01
MacMahon, P. A.
1908
Second memoir on the compositions of numbers. JFM 38.0225.01
MacMahon, P. A.
1907
The sums of powers of the binomial coefficients. JFM 33.0285.05
MacMahon, P. A.
1902
Combinatorial analysis. JFM 31.0219.01
MacMahon, P. A.
1900
Partitions of numbers whose graphs possess symmetry. JFM 30.0201.04
MacMahon, P. A.
1899
Memoir on the theory of the partitions of numbers. Part. II. JFM 30.0171.11
MacMahon, P. A.
1899
A new method in combinatory analysis, with application to latin squares and associated questions. JFM 30.0227.11
MacMahon, P. A.
1898
Combinatory analysis: a review of the present state of knowledge. JFM 28.0103.01
MacMahon, P. A.
1897
Memoir on the theory of the partition of numbers. Part I. JFM 27.0134.04
MacMahon, P. A.
1896
James Joseph Sylvester. JFM 28.0030.03
MacMahon, P. A.
1896
The perpetuant invariants of binary quantics. JFM 26.0141.01
MacMahon, P. A.
1895
Memoir on the theory of the compositions of numbers. JFM 25.0258.01
MacMahon, P. A.
1893
A certain class of generating functions in the theory of numbers. JFM 25.0258.02
MacMahon, P. A.
1893
Application of a theory of permutations in circular precession to the theory of numbers. JFM 24.0181.01
MacMahon, P. A.
1892
Yoke-chains and multipartite compositions in connexion with the analytical forms called “trees”. JFM 23.0132.02
MacMahon, P. A.
1891
Yoke-chains and multipartite compositions in connexion with the analytical forms called trees. JFM 23.0565.02
MacMahon, P. A.
1891
Memoir on the symmetric functions of the roots of equations. JFM 22.0187.02
MacMahon, P. A.
1890
Weighing by a series of weights. JFM 23.0186.03
MacMahon, P. A.
1890
Certain special partitions of numbers. JFM 18.0138.04
MacMahon, P. A.
1886
A second paper on perpetuants. JFM 17.0082.03
MacMahon, P. A.
1885
Seminvariants and symmetric functions. JFM 15.0127.01
MacMahon, P. A.
1883
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#### Cited by 776 Authors

 18 Krattenthaler, Christian Friedrich 16 Andrews, George Eyre 16 Ciucu, Mihai 16 Foata, Dominique C. 14 Lai, Tri 11 Ehrenborg, Richard 11 Sills, Andrew V. 11 Zeilberger, Doron 10 Rawlings, Don 9 Chen, William Yong-Chuan 9 Han, Guo-Niu 9 Jackson, David M. 9 Merca, Mircea 9 Stanley, Richard Peter 8 Biagioli, Riccardo 7 Carlitz, Leonard 7 Gessel, Ira Martin 7 Konvalinka, Matjaž 7 Roichman, Yuval 7 Zeng, Jiang 6 Caselli, Fabrizio 6 Goulden, Ian P. 6 Mansour, Toufik 6 Munagi, Augustine O. 6 Sagan, Bruce Eli 6 Savage, Carla D. 6 Wachs, Michelle Lynn 5 Drensky, Vesselin 5 Readdy, Margaret A. 5 Remmel, Jeffrey B. 5 Swanson, Joshua P. 5 Viennot, Xavier Gérard 4 Adin, Ron M. 4 Agarwal, Ashwani Kumar 4 Brenti, Francesco 4 Clarke, Robert J. 4 Eisenkölbl, Theresia 4 Fischer, Ilse 4 Milne, Stephen C. 4 Pak, Igor 4 Park, SeungKyung 4 Riordan, John F. 4 Rohatgi, Ranjan 4 Rosas, Mercedes Helena 4 Stein, Paul R. 4 Sulanke, Robert A. 4 Warnaar, S. Ole 3 Abramson, Morton 3 Beck, Matthias 3 Billey, Sara C. 3 Borodin, Alexei 3 Cerasoli, Mauro 3 Chu, Wenchang 3 Del Lungo, Alberto 3 Eu, Sen-Peng 3 Fındık, Şehmus 3 Good, Irving John (Jack) 3 Gordon, Basil 3 Haglund, James 3 Hernane, Mohand-Ouamar 3 Knopfmacher, Arnold 3 Lin, Zhicong 3 Lovejoy, Jeremy 3 Mathieu, Pierre 3 Mutafchiev, Lyuben R. 3 Nicolas, Jean-Louis 3 Niederhausen, Heinrich 3 Regev, Amitai 3 Rhoades, Brendon 3 Steingrímsson, Einar 3 Tewari, Vasu V. 3 Vallejo, Ernesto 3 Van Willigenburg, Stephanie J. 3 Yee, Ae Ja 2 Adler, Mark 2 Ahlbach, Connor 2 Armstrong, Drew 2 Assaf, Sami H. 2 Bayad, Abdelmejid 2 Bell, Eric Temple 2 Berkovich, Alexander 2 Björner, Anders 2 Braun, Benjamin 2 Bressoud, David M. 2 Brini, Andrea 2 Brunetti, Sara 2 Canfield, E. Rodney 2 Choliy, Yuriy 2 Chung Graham, Fan-Rong King 2 Colmenarejo, Laura 2 Conflitti, Alessandro 2 Conger, Mark A. 2 Corteel, Sylvie 2 Crilly, Tony 2 Dangovski, Rumen 2 Désarménien, Jacques 2 Destainville, Nicolas 2 Domokos, Mátyás 2 Edmonds, Frances Chevarley 2 Ewell, John A. ...and 676 more Authors
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#### Cited in 147 Serials

 102 Journal of Combinatorial Theory. Series A 84 Discrete Mathematics 55 Advances in Applied Mathematics 40 European Journal of Combinatorics 25 Advances in Mathematics 20 Annals of Combinatorics 19 Proceedings of the American Mathematical Society 16 Journal of Number Theory 16 The Ramanujan Journal 15 Journal of Algebra 14 Transactions of the American Mathematical Society 13 Linear Algebra and its Applications 11 Journal of Algebraic Combinatorics 8 Journal of Integer Sequences 7 Journal of Mathematical Analysis and Applications 7 Journal of Statistical Planning and Inference 7 Séminaire Lotharingien de Combinatoire 7 International Journal of Number Theory 6 Nuclear Physics. B 6 Mathematics of Computation 6 Theoretical Computer Science 5 Discrete Applied Mathematics 5 Journal of Mathematical Physics 5 The Electronic Journal of Combinatorics 5 Integers 4 Journal of Combinatorial Theory. Series B 4 Mathematische Annalen 4 Studies in Applied Mathematics 3 Israel Journal of Mathematics 3 Journal of Statistical Physics 3 The Mathematical Intelligencer 3 Inventiones Mathematicae 3 Journal of Computational and Applied Mathematics 3 Statistics & Probability Letters 3 Journal of Symbolic Computation 3 Discrete & Computational Geometry 3 SIAM Journal on Discrete Mathematics 3 Aequationes Mathematicae 3 Historia Mathematica 3 Journal of Mathematical Sciences (New York) 3 Annales de l’Institut Henri Poincaré D. Combinatorics, Physics and their Interactions (AIHPD) 2 International Journal of Modern Physics B 2 Computers & Mathematics with Applications 2 Communications in Mathematical Physics 2 Physica A 2 Rocky Mountain Journal of Mathematics 2 Journal of Geometry and Physics 2 Biometrical Journal 2 Duke Mathematical Journal 2 Manuscripta Mathematica 2 Mathematische Nachrichten 2 Quaestiones Mathematicae 2 Rendiconti del Circolo Matemàtico di Palermo. Serie II 2 Mathematical and Computer Modelling 2 Bulletin of the American Mathematical Society. New Series 2 Proceedings of the Indian Academy of Sciences. Mathematical Sciences 2 Indagationes Mathematicae. New Series 2 Journal de Théorie des Nombres de Bordeaux 2 Combinatorics, Probability and Computing 2 Journal of Algebra and its Applications 2 Mediterranean Journal of Mathematics 2 Bulletin of the American Mathematical Society 2 Contributions to Discrete Mathematics 2 Forum of Mathematics, Sigma 2 Algebraic Combinatorics 1 American Mathematical Monthly 1 Analysis Mathematica 1 Applicable Analysis 1 Bulletin of the Australian Mathematical Society 1 Communications in Algebra 1 Indian Journal of Pure & Applied Mathematics 1 Journal of the Franklin Institute 1 Lithuanian Mathematical Journal 1 Linear and Multilinear Algebra 1 The Mathematical Gazette 1 Mathematical Notes 1 Mathematical Proceedings of the Cambridge Philosophical Society 1 Periodica Mathematica Hungarica 1 Theoretical and Mathematical Physics 1 Ukrainian Mathematical Journal 1 Abhandlungen aus dem Mathematischen Seminar der Universität Hamburg 1 Algebra Universalis 1 Annali di Matematica Pura ed Applicata. Serie Quarta 1 The Annals of Probability 1 The Annals of Statistics 1 Annales Scientifiques de l’Université de Clermont-Ferrand II. Mathématiques 1 Archiv der Mathematik 1 Functiones et Approximatio. Commentarii Mathematici 1 Functional Analysis and its Applications 1 Fuzzy Sets and Systems 1 Integral Equations and Operator Theory 1 Journal of Differential Equations 1 Journal of Multivariate Analysis 1 Journal of Pure and Applied Algebra 1 Matematički Vesnik 1 Memoirs of the American Mathematical Society 1 Numerische Mathematik 1 Programming and Computer Software 1 Rendiconti del Seminario Matematico della Università di Padova 1 Zeitschrift für Wahrscheinlichkeitstheorie und Verwandte Gebiete ...and 47 more Serials
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#### Cited in 47 Fields

 546 Combinatorics (05-XX) 193 Number theory (11-XX) 57 Group theory and generalizations (20-XX) 43 Special functions (33-XX) 37 Linear and multilinear algebra; matrix theory (15-XX) 35 Convex and discrete geometry (52-XX) 33 Order, lattices, ordered algebraic structures (06-XX) 31 Probability theory and stochastic processes (60-XX) 21 Commutative algebra (13-XX) 19 Computer science (68-XX) 18 Quantum theory (81-XX) 18 Statistical mechanics, structure of matter (82-XX) 17 Algebraic geometry (14-XX) 15 Associative rings and algebras (16-XX) 12 History and biography (01-XX) 11 Nonassociative rings and algebras (17-XX) 9 Functions of a complex variable (30-XX) 7 Statistics (62-XX) 6 Real functions (26-XX) 5 Ordinary differential equations (34-XX) 5 Difference and functional equations (39-XX) 4 General and overarching topics; collections (00-XX) 4 Category theory; homological algebra (18-XX) 4 Topological groups, Lie groups (22-XX) 4 Numerical analysis (65-XX) 3 Operator theory (47-XX) 3 Manifolds and cell complexes (57-XX) 3 Game theory, economics, finance, and other social and behavioral sciences (91-XX) 3 Information and communication theory, circuits (94-XX) 2 Mathematical logic and foundations (03-XX) 2 Field theory and polynomials (12-XX) 2 Dynamical systems and ergodic theory (37-XX) 2 Approximations and expansions (41-XX) 2 Harmonic analysis on Euclidean spaces (42-XX) 2 Functional analysis (46-XX) 2 Operations research, mathematical programming (90-XX) 2 Biology and other natural sciences (92-XX) 2 Systems theory; control (93-XX) 1 Several complex variables and analytic spaces (32-XX) 1 Partial differential equations (35-XX) 1 Integral transforms, operational calculus (44-XX) 1 Integral equations (45-XX) 1 Geometry (51-XX) 1 Differential geometry (53-XX) 1 Algebraic topology (55-XX) 1 Global analysis, analysis on manifolds (58-XX) 1 Mechanics of deformable solids (74-XX)

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