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Garvan, Frank G.

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Author ID: garvan.frank-g Recent zbMATH articles by "Garvan, Frank G."
Published as: Garvan, F.; Garvan, F. G.; Garvan, Frank; Garvan, Frank G.
External Links: MGP · Wikidata
Documents Indexed: 64 Publications since 1984, including 7 Books

Publications by Year

Citations contained in zbMATH

56 Publications have been cited 1,053 times in 602 Documents Cited by Year
Dyson’s crank of a partition. Zbl 0646.10008
Andrews, George E.; Garvan, F. G.
131
1988
Cranks and t-cores. Zbl 0721.11039
Garvan, Frank; Kim, Dongsu; Stanton, Dennis
129
1990
New combinatorial interpretations of Ramanujan’s partition congruences mod \(5, 7\) and \(11\). Zbl 0641.10009
Garvan, F. G.
89
1988
Ramanujan’s theories of elliptic functions to alternative bases. Zbl 0843.33012
Berndt, Bruce C.; Bhargava, S.; Garvan, Frank G.
79
1995
Cubic analogues of the Jacobian theta function \(\theta(z,q)\). Zbl 0797.33012
Hirschhorn, Michael; Garvan, Frank; Borwein, Jon
60
1993
Some cubic modular identities of Ramanujan. Zbl 0799.33012
Borwein, J. M.; Borwein, P. B.; Garvan, F. G.
51
1994
Relations between the ranks and cranks of partitions. Zbl 1039.11069
Atkin, A. O. L.; Garvan, F. G.
44
2003
Some observations on Dyson’s new symmetries of partitions. Zbl 1016.05003
Berkovich, Alexander; Garvan, Frank G.
43
2002
Congruences for Andrews’ smallest parts partition function and new congruences for Dyson’s rank. Zbl 1219.11153
Garvan, F. G.
36
2010
Higher order spt-functions. Zbl 1268.11143
Garvan, F. G.
34
2011
Ramanujan’s “Lost” Notebook. VI: The mock theta conjectures. Zbl 0677.10010
Andrews, George E.; Garvan, F. G.
26
1989
Some congruences for partitions that are \(p\)-cores. Zbl 0788.11044
Garvan, Frank G.
21
1993
A simple proof of Watson’s partition congruences for powers of 7. Zbl 0533.10006
Garvan, F. G.
19
1984
Generalization of Dyson’s rank and non-Rogers-Ramanujan partitions. Zbl 0819.11043
Garvan, Frank G.
18
1994
Combinatorial interpretations of congruences for the spt-function. Zbl 1256.05012
Andrews, George E.; Garvan, Frank G.; Liang, Jie
17
2012
Partition statistics and quasiharmonic Maass forms. Zbl 1156.11021
Bringmann, Kathrin; Garvan, Frank; Mahlburg, Karl
17
2009
The spt-crank for overpartitions. Zbl 1316.11093
Garvan, Frank G.; Jennings-Shaffer, Chris
16
2014
The crank of partitions mod 8, 9 and 10. Zbl 0717.11042
Garvan, Frank G.
16
1990
Congruences for Andrews spt-function modulo powers of \(5, 7\) and \(13\). Zbl 1286.11165
Garvan, F. G.
15
2012
The Maple book. Zbl 1005.68185
Garvan, Frank
13
2001
Self-conjugate vector partitions and the parity of the spt-function. Zbl 1268.05019
Andrews, George E.; Garvan, Frank G.; Liang, Jie
12
2013
On the Andrews-Stanley refinement of Ramanujan’s partition congruence modulo \(5\) and generalizations. Zbl 1088.11073
Berkovich, Alexander; Garvan, Frank G.
11
2006
Sieved partition functions and q-binomial coefficients. Zbl 0702.05008
Garvan, Frank; Stanton, Dennis
11
1990
Congruences for generalized Frobenius partitions with an arbitrarily large number of colors. Zbl 1284.11136
Garvan, Frank G.; Sellers, James A.
10
2014
Combinatorial interpretations of Ramanujan’s partition congruences. Zbl 0652.10010
Garvan, F. G.
10
1988
Macdonald’s constant term conjectures for exceptional root systems. Zbl 0737.33011
Garvan, Frank G.; Gonnet, Gaston
9
1991
More cranks and \(t\)-cores. Zbl 0985.11050
Garvan, F. G.
8
2001
Exotic Bailey-Slater spt-functions. II: Hecke-Rogers-type double sums and Bailey pairs from groups A, C, E. Zbl 1348.11079
Garvan, F. G.; Jennings-Shaffer, C.
7
2016
Universal mock theta functions and two-variable Hecke-Rogers identities. Zbl 1380.11091
Garvan, F. G.
7
2015
Approximations to \(\pi\) via the Dedekind eta function. Zbl 0893.11050
Borwein, J. M.; Garvan, F. G.
7
1997
A proof of the Macdonald-Morris root system conjecture for \(F_ 4\). Zbl 0711.33001
Garvan, F. G.
7
1990
Biranks for partitions into 2 colors. Zbl 1267.11109
Garvan, F. G.
6
2010
The BG-rank of a partition and its applications. Zbl 1228.11159
Berkovich, Alexander; Garvan, Frank G.
6
2008
Dissecting the Stanley partition function. Zbl 1142.05001
Berkovich, Alexander; Garvan, Frank G.
6
2005
Qseries Maple tutorial: A \(q\)-product tutorial for a \(q\)-series Maple package. Zbl 1010.11072
Garvan, Frank
6
1999
Hypergeometric analogues of the arithmetic-geometric mean iteration. Zbl 0785.33001
Borwein, J.; Borwein, P.; Garvan, F.
5
1993
Some Macdonald-Mehta integrals by brute force. Zbl 0697.33008
Garvan, Frank G.
5
1989
Congruences and relations for \(r\)-Fishburn numbers. Zbl 1315.05013
Garvan, F. G.
4
2015
Rank-crank-type PDEs and generalized Lambert series identities. Zbl 1328.11053
Chan, Song Heng; Dixit, Atul; Garvan, Frank G.
4
2013
K. Saito’s Conjecture for nonnegative eta products and analogous results for other infinite products. Zbl 1143.05008
Berkovich, Alexander; Garvan, Frank G.
4
2008
A generalization of the Hirschhorn-Farkas-Kra septagonal numbers identity. Zbl 0979.05009
Garvan, F. G.
4
2001
Cubic modular identities of Ramanujan, hypergeometric functions and analogues of the arithmetic-geometric mean iteration. Zbl 0808.33003
Garvan, Frank
4
1994
A proof of the two parameter \(q\)-cases of the Macdonald-Morris constant term root system conjecture for \(S(F_ 4)\) and \(S(F_ 4)^ \vee\) via Zeilberger’s method. Zbl 0766.33017
Garvan, Frank G.; Gonnet, Gaston H.
4
1992
Transformation properties for Dyson’s rank function. Zbl 06993232
Garvan, F. G.
3
2019
Ramanujan’s theories of elliptic functions to alternative bases – A symbolic excursion. Zbl 0849.68063
Garvan, Frank G.
3
1995
A beta integral associated with the root system \(G_ 2\). Zbl 0657.33001
Garvan, F. G.
3
1988
Weighted partition identities and divisor sums. Zbl 07059294
Garvan, F. G.
2
2018
Congruences for Andrews’ spt-function modulo 32760 and extension of Atkin’s Hecke-type partition congruences. Zbl 1286.11164
Garvan, F. G.
2
2013
Shifted and shiftless partition identities. II. Zbl 1125.11057
Garvan, Frank G.; Yesilyurt, Hamza
2
2007
New fifth and seventh order mock theta function identities. Zbl 1439.11120
Garvan, Frank G.
1
2019
Hecke-type congruences for Andrews’ spt-function modulo \(16\) and \(32\). Zbl 1286.11166
Garvan, Frank G.; Jennings-Shaffer, Chris
1
2014
Computational and analytical mathematics. In Honor of Jonathan Borwein’s 60th birthday. Selected papers based on the presentations at the workshop, also known as JonFest, Simon Fraser University, BC, Canada, May 16–20, 2011. Zbl 1276.00018
Bailey, David H. (ed.); Bauschke, Heinz H. (ed.); Borwein, Peter (ed.); Garvan, Frank (ed.); Théra, Michel (ed.); Vanderwerff, Jon D. (ed.); Wolkowicz, Henry (ed.)
1
2013
Partitions, \(q\)-series, and modular forms. Based on the conference, Gainesville, FL, USA, March 8–16, 2008. Zbl 1230.11003
Alladi, Krishnaswami (ed.); Garvan, Frank (ed.)
1
2012
The GBG-rank and \(t\)-cores. I: Counting and 4-cores. Zbl 1258.11090
Berkovich, Alexander; Garvan, Frank G.
1
2009
Shifted and shiftless partition identities. Zbl 1035.11050
Garvan, F. G.
1
2002
Maple V primer, release 4. Zbl 0855.68045
Garvan, Frank
1
1997
Transformation properties for Dyson’s rank function. Zbl 06993232
Garvan, F. G.
3
2019
New fifth and seventh order mock theta function identities. Zbl 1439.11120
Garvan, Frank G.
1
2019
Weighted partition identities and divisor sums. Zbl 07059294
Garvan, F. G.
2
2018
Exotic Bailey-Slater spt-functions. II: Hecke-Rogers-type double sums and Bailey pairs from groups A, C, E. Zbl 1348.11079
Garvan, F. G.; Jennings-Shaffer, C.
7
2016
Universal mock theta functions and two-variable Hecke-Rogers identities. Zbl 1380.11091
Garvan, F. G.
7
2015
Congruences and relations for \(r\)-Fishburn numbers. Zbl 1315.05013
Garvan, F. G.
4
2015
The spt-crank for overpartitions. Zbl 1316.11093
Garvan, Frank G.; Jennings-Shaffer, Chris
16
2014
Congruences for generalized Frobenius partitions with an arbitrarily large number of colors. Zbl 1284.11136
Garvan, Frank G.; Sellers, James A.
10
2014
Hecke-type congruences for Andrews’ spt-function modulo \(16\) and \(32\). Zbl 1286.11166
Garvan, Frank G.; Jennings-Shaffer, Chris
1
2014
Self-conjugate vector partitions and the parity of the spt-function. Zbl 1268.05019
Andrews, George E.; Garvan, Frank G.; Liang, Jie
12
2013
Rank-crank-type PDEs and generalized Lambert series identities. Zbl 1328.11053
Chan, Song Heng; Dixit, Atul; Garvan, Frank G.
4
2013
Congruences for Andrews’ spt-function modulo 32760 and extension of Atkin’s Hecke-type partition congruences. Zbl 1286.11164
Garvan, F. G.
2
2013
Computational and analytical mathematics. In Honor of Jonathan Borwein’s 60th birthday. Selected papers based on the presentations at the workshop, also known as JonFest, Simon Fraser University, BC, Canada, May 16–20, 2011. Zbl 1276.00018
Bailey, David H. (ed.); Bauschke, Heinz H. (ed.); Borwein, Peter (ed.); Garvan, Frank (ed.); Théra, Michel (ed.); Vanderwerff, Jon D. (ed.); Wolkowicz, Henry (ed.)
1
2013
Combinatorial interpretations of congruences for the spt-function. Zbl 1256.05012
Andrews, George E.; Garvan, Frank G.; Liang, Jie
17
2012
Congruences for Andrews spt-function modulo powers of \(5, 7\) and \(13\). Zbl 1286.11165
Garvan, F. G.
15
2012
Partitions, \(q\)-series, and modular forms. Based on the conference, Gainesville, FL, USA, March 8–16, 2008. Zbl 1230.11003
Alladi, Krishnaswami (ed.); Garvan, Frank (ed.)
1
2012
Higher order spt-functions. Zbl 1268.11143
Garvan, F. G.
34
2011
Congruences for Andrews’ smallest parts partition function and new congruences for Dyson’s rank. Zbl 1219.11153
Garvan, F. G.
36
2010
Biranks for partitions into 2 colors. Zbl 1267.11109
Garvan, F. G.
6
2010
Partition statistics and quasiharmonic Maass forms. Zbl 1156.11021
Bringmann, Kathrin; Garvan, Frank; Mahlburg, Karl
17
2009
The GBG-rank and \(t\)-cores. I: Counting and 4-cores. Zbl 1258.11090
Berkovich, Alexander; Garvan, Frank G.
1
2009
The BG-rank of a partition and its applications. Zbl 1228.11159
Berkovich, Alexander; Garvan, Frank G.
6
2008
K. Saito’s Conjecture for nonnegative eta products and analogous results for other infinite products. Zbl 1143.05008
Berkovich, Alexander; Garvan, Frank G.
4
2008
Shifted and shiftless partition identities. II. Zbl 1125.11057
Garvan, Frank G.; Yesilyurt, Hamza
2
2007
On the Andrews-Stanley refinement of Ramanujan’s partition congruence modulo \(5\) and generalizations. Zbl 1088.11073
Berkovich, Alexander; Garvan, Frank G.
11
2006
Dissecting the Stanley partition function. Zbl 1142.05001
Berkovich, Alexander; Garvan, Frank G.
6
2005
Relations between the ranks and cranks of partitions. Zbl 1039.11069
Atkin, A. O. L.; Garvan, F. G.
44
2003
Some observations on Dyson’s new symmetries of partitions. Zbl 1016.05003
Berkovich, Alexander; Garvan, Frank G.
43
2002
Shifted and shiftless partition identities. Zbl 1035.11050
Garvan, F. G.
1
2002
The Maple book. Zbl 1005.68185
Garvan, Frank
13
2001
More cranks and \(t\)-cores. Zbl 0985.11050
Garvan, F. G.
8
2001
A generalization of the Hirschhorn-Farkas-Kra septagonal numbers identity. Zbl 0979.05009
Garvan, F. G.
4
2001
Qseries Maple tutorial: A \(q\)-product tutorial for a \(q\)-series Maple package. Zbl 1010.11072
Garvan, Frank
6
1999
Approximations to \(\pi\) via the Dedekind eta function. Zbl 0893.11050
Borwein, J. M.; Garvan, F. G.
7
1997
Maple V primer, release 4. Zbl 0855.68045
Garvan, Frank
1
1997
Ramanujan’s theories of elliptic functions to alternative bases. Zbl 0843.33012
Berndt, Bruce C.; Bhargava, S.; Garvan, Frank G.
79
1995
Ramanujan’s theories of elliptic functions to alternative bases – A symbolic excursion. Zbl 0849.68063
Garvan, Frank G.
3
1995
Some cubic modular identities of Ramanujan. Zbl 0799.33012
Borwein, J. M.; Borwein, P. B.; Garvan, F. G.
51
1994
Generalization of Dyson’s rank and non-Rogers-Ramanujan partitions. Zbl 0819.11043
Garvan, Frank G.
18
1994
Cubic modular identities of Ramanujan, hypergeometric functions and analogues of the arithmetic-geometric mean iteration. Zbl 0808.33003
Garvan, Frank
4
1994
Cubic analogues of the Jacobian theta function \(\theta(z,q)\). Zbl 0797.33012
Hirschhorn, Michael; Garvan, Frank; Borwein, Jon
60
1993
Some congruences for partitions that are \(p\)-cores. Zbl 0788.11044
Garvan, Frank G.
21
1993
Hypergeometric analogues of the arithmetic-geometric mean iteration. Zbl 0785.33001
Borwein, J.; Borwein, P.; Garvan, F.
5
1993
A proof of the two parameter \(q\)-cases of the Macdonald-Morris constant term root system conjecture for \(S(F_ 4)\) and \(S(F_ 4)^ \vee\) via Zeilberger’s method. Zbl 0766.33017
Garvan, Frank G.; Gonnet, Gaston H.
4
1992
Macdonald’s constant term conjectures for exceptional root systems. Zbl 0737.33011
Garvan, Frank G.; Gonnet, Gaston
9
1991
Cranks and t-cores. Zbl 0721.11039
Garvan, Frank; Kim, Dongsu; Stanton, Dennis
129
1990
The crank of partitions mod 8, 9 and 10. Zbl 0717.11042
Garvan, Frank G.
16
1990
Sieved partition functions and q-binomial coefficients. Zbl 0702.05008
Garvan, Frank; Stanton, Dennis
11
1990
A proof of the Macdonald-Morris root system conjecture for \(F_ 4\). Zbl 0711.33001
Garvan, F. G.
7
1990
Ramanujan’s “Lost” Notebook. VI: The mock theta conjectures. Zbl 0677.10010
Andrews, George E.; Garvan, F. G.
26
1989
Some Macdonald-Mehta integrals by brute force. Zbl 0697.33008
Garvan, Frank G.
5
1989
Dyson’s crank of a partition. Zbl 0646.10008
Andrews, George E.; Garvan, F. G.
131
1988
New combinatorial interpretations of Ramanujan’s partition congruences mod \(5, 7\) and \(11\). Zbl 0641.10009
Garvan, F. G.
89
1988
Combinatorial interpretations of Ramanujan’s partition congruences. Zbl 0652.10010
Garvan, F. G.
10
1988
A beta integral associated with the root system \(G_ 2\). Zbl 0657.33001
Garvan, F. G.
3
1988
A simple proof of Watson’s partition congruences for powers of 7. Zbl 0533.10006
Garvan, F. G.
19
1984
all top 5

Cited by 495 Authors

26 Garvan, Frank G.
22 Bringmann, Kathrin
22 Kim, Byungchan
17 Jennings-Shaffer, Chris
16 Mao, Renrong
16 Ono, Ken
15 Andrews, George Eyre
15 Baruah, Nayandeep Deka
15 Berkovich, Alexander
15 Chan, Heng Huat
15 Lovejoy, Jeremy
15 Xia, Ernest X. W.
13 Wang, Liuquan
12 Cooper, Shaun
12 Hirschhorn, Michael D.
11 Chan, Song Heng
9 Ahlgren, Scott D.
9 Chu, Yuming
9 Mahadeva Naika, Megadahalli Sidda
9 Qiu, Songliang
9 Rhoades, Robert C.
9 Yao, Olivia Xiang Mei
8 Ji, Kathy Qing
8 Osburn, Robert
8 Sellers, James Allen
7 Folsom, Amanda
7 Liu, Zhi-Guo
7 Tang, Dazhao
7 Vuorinen, Matti Keijo Kustaa
6 Berndt, Bruce Carl
6 Chern, Shane
6 Lin, Bernard L. S.
6 Mahlburg, Karl
6 Saikia, Nipen
6 Shen, Lichien
6 Swisher, Holly
6 Toh, Pee Choon
6 Zhang, Xiaohui
5 Andersen, Nickolas
5 Cui, Su-Ping
5 Dixit, Atul
5 Ito, Masahiko
5 Ma, Xiaoyan
5 Merca, Mircea
5 Nath, Kallol
5 Warnaar, S. Ole
5 Ye, Dongxi
5 Yesilyurt, Hamza
5 Zeilberger, Doron
4 Boylan, Matthew
4 Chu, Wenchang
4 Gireesh, D. S.
4 Gu, Nancy Shan Shan
4 Han, Guo-Niu
4 Huber, Tim
4 Kang, Soon-Yi
4 Lemonte, Artur José
4 Liaw, Wen-Chin
4 Mortenson, Eric T.
4 Nath, Rishi
4 Patkowski, Alexander Eric
4 Uncu, Ali Kemal
4 Wang, Miaokun
4 Yee, Ae Ja
3 Adiga, Chandrashekar
3 Ahmed, Zakir Hussain
3 Alladi, Krishnaswami
3 Anderson, Glen Douglas
3 Balasubramanian, Ramachandran
3 Chen, Shichao
3 Chen, William Yong-Chuan
3 Chetry, Jubaraj
3 Cordeiro, Gauss Moutinho
3 da Silva, Robson
3 Dyson, Freeman John
3 Fathima, Syeda Noor
3 Fu, Shishuo
3 Hao, Li-Jun
3 Heim, Bernhard Ernst
3 Hickerson, Dean R.
3 Jang, Min-Joo
3 Kane, Ben
3 Kim, Eunmi
3 Kimport, Sam
3 Kolitsch, Louis Worthy
3 Nayaka, S. Shivaprasada
3 Neuhauser, Markus
3 Olsson, Jørn Børling
3 Ponnusamy, Saminathan
3 Rolen, Larry
3 Shivashankar, Chandrappa
3 Solé, Patrick
3 Sze, Lawrence
3 Wang, Chun
3 Wang, Gendi
3 Xiong, Huan
3 Zhang, Helen W. J.
3 Zhang, Wenlong
3 Zhao, Alice Xiao Hua
3 Zhou, Nian Hong
...and 395 more Authors
all top 5

Cited in 122 Serials

91 The Ramanujan Journal
61 Journal of Number Theory
36 Journal of Mathematical Analysis and Applications
34 Journal of Combinatorial Theory. Series A
33 International Journal of Number Theory
29 Advances in Mathematics
26 Discrete Mathematics
23 Transactions of the American Mathematical Society
21 Proceedings of the American Mathematical Society
17 Annals of Combinatorics
11 Bulletin of the Australian Mathematical Society
7 Acta Arithmetica
7 Inventiones Mathematicae
7 Advances in Applied Mathematics
7 Research in the Mathematical Sciences
7 Research in Number Theory
6 Proceedings of the National Academy of Sciences of the United States of America
6 Bulletin of the American Mathematical Society. New Series
6 Proceedings of the Indian Academy of Sciences. Mathematical Sciences
4 Archiv der Mathematik
4 European Journal of Combinatorics
4 Journal of Algebraic Combinatorics
4 Acta Mathematica Sinica. English Series
4 Integers
4 Afrika Matematika
3 Communications in Mathematical Physics
3 Indian Journal of Pure & Applied Mathematics
3 Mathematical Notes
3 Rocky Mountain Journal of Mathematics
3 Journal of Algebra
3 Journal of Symbolic Computation
3 Turkish Journal of Mathematics
3 The Electronic Journal of Combinatorics
3 Séminaire Lotharingien de Combinatoire
3 Brazilian Journal of Probability and Statistics
2 American Mathematical Monthly
2 Israel Journal of Mathematics
2 Mathematical Proceedings of the Cambridge Philosophical Society
2 Acta Mathematica Vietnamica
2 Applied Mathematics and Computation
2 Journal of Approximation Theory
2 Journal für die Reine und Angewandte Mathematik
2 Manuscripta Mathematica
2 Nagoya Mathematical Journal
2 Quaestiones Mathematicae
2 Studies in Applied Mathematics
2 Theoretical Computer Science
2 International Journal of Computer Mathematics
2 Applied Mathematics. Series B (English Edition)
2 Journal de Théorie des Nombres de Bordeaux
2 Mathematical Inequalities & Applications
2 Journal of Integer Sequences
2 SIGMA. Symmetry, Integrability and Geometry: Methods and Applications
2 Mathematics
2 Open Mathematics
2 Korean Journal of Mathematics
1 Communications in Algebra
1 Discrete Applied Mathematics
1 Journal of Mathematical Physics
1 Letters in Mathematical Physics
1 Lithuanian Mathematical Journal
1 Nuclear Physics. B
1 Physics Letters. A
1 Ukrainian Mathematical Journal
1 Mathematics of Computation
1 Annales de l’Institut Fourier
1 Compositio Mathematica
1 Duke Mathematical Journal
1 Journal of Computational and Applied Mathematics
1 The Journal of the Indian Mathematical Society. New Series
1 Journal of the London Mathematical Society. Second Series
1 Journal of Optimization Theory and Applications
1 Mathematische Annalen
1 Mathematische Nachrichten
1 Monatshefte für Mathematik
1 Osaka Journal of Mathematics
1 Proceedings of the Edinburgh Mathematical Society. Series II
1 Publications of the Research Institute for Mathematical Sciences, Kyoto University
1 Rendiconti del Circolo Matemàtico di Palermo. Serie II
1 Note di Matematica
1 Statistics
1 Journal of the American Mathematical Society
1 Journal of the Ramanujan Mathematical Society
1 Differential Geometry and its Applications
1 Aequationes Mathematicae
1 Expositiones Mathematicae
1 The Australasian Journal of Combinatorics
1 Experimental Mathematics
1 Finite Fields and their Applications
1 Selecta Mathematica. New Series
1 Boletín de la Sociedad Matemática Mexicana. Third Series
1 Electronic Research Announcements of the American Mathematical Society
1 The Journal of Fourier Analysis and Applications
1 Vietnam Journal of Mathematics
1 Mathematical Physics, Analysis and Geometry
1 Journal of Discrete Mathematical Sciences & Cryptography
1 European Journal of Mechanics. A. Solids
1 Annals of Mathematics. Second Series
1 Communications in Contemporary Mathematics
1 Journal of High Energy Physics
...and 22 more Serials

Citations by Year

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