zbMATH — the first resource for mathematics

Two combinatorial applications of the Aleksandrov-Fenchel inequalities. (English) Zbl 0484.05012

05A20 Combinatorial inequalities
05B35 Combinatorial aspects of matroids and geometric lattices
52Bxx Polytopes and polyhedra
Full Text: DOI Link
[1] Aleksandrov, A.D; Aleksandrov, A.D; Aleksandrov, A.D; Aleksandrov, A.D, “zur theorie der gemischten volumina von konvexen Körpern,” Russian, German summaries, parts I, II, III, IV. IV. die gemischten diskriminanten und die gemischten volumina, Mat. sbornik N.S., Mat. sbornik N.S., Mat. sbornik N.S., Mat. sbornik N.S., 3, 227-251, (1938) · Zbl 0019.32804
[2] Biggs, N, Algebraic graph theory, (1974), Cambridge Univ. Press Cambridge · Zbl 0284.05101
[3] Bonnesen, J; Fenchel, W, Theorie der konvexen Körper, (1934), Springer Berlin, or New York, 1948 · Zbl 0008.07708
[4] Busemann, H, Convex surfaces, (1958), Interscience New York · Zbl 0196.55101
[5] Chung, F.R.K; Fishburn, P.C; Graham, R.L, On unimodality for linear extensions of partial orders, SIAM J. algebraic and discrete methods, 1, 405-410, (1980) · Zbl 0501.06005
[6] Crapo, H.H; Rota, G.-C, On the foundations of combinatorial theory: combinatorial geometries, (1976), MIT Press Cambridge, Mass · Zbl 0216.02101
[7] {\scT. A. Dowling}, On the independent set numbers of a finite matroid, preprint. · Zbl 0462.05020
[8] Eggleston, H.G, Convexity, (1958), Cambridge Univ. Press Cambridge · Zbl 0086.15302
[9] Fenchel, W, Inégalités quadratiques entre LES volumes mixtes des corps convexes, C. R. acad. sci. Paris, 203, 647-650, (1936) · JFM 62.0833.02
[10] Fenchel, W, Généralizations du théorème de brunn et Minkowski concernant LES corps convexes, C. R. acad. sci. Paris, 203, 764-766, (1936) · JFM 62.0833.03
[11] Graham, R.L; Yao, A.C; Yao, F.F, Some monotonicity properties of partial orders, SIAM J. algebraic and discrete methods, 1, 251-258, (1980) · Zbl 0496.68043
[12] Mason, J.H, Matroids: unimodal conjectures and Motzkin’s theorem, (), 207-221
[13] Phedotov, V.P, A new method of proving inequalities between mixed volumes, and a generalization of the Aleksandrov-Fenchel-shephard inequalities, Soviet math. dokl., 20, 268-271, (1979) · Zbl 0432.52007
[14] Seymour, P.D; Welsh, D.J.A, Combinatorial applications of an inequality from statistical mechanics, (), 485-495 · Zbl 0345.05004
[15] Shephard, G.C, Inequalities between mixed volumes of convex sets, Mathematika, 7, 125-138, (1960) · Zbl 0108.35203
[16] Shephard, G.C, Combinatorial properties of associated zonotopes, Canad. J. math., 26, 302-321, (1974) · Zbl 0287.52005
[17] Shepp, L.A, The FKG inequality and some monotonicity properties of partial orders, SIAM J. algebraic and discrete methods, 1, 295-299, (1980) · Zbl 0501.06006
[18] Teissier, B, Du théorème de l’index de Hodge aux inégalités isopérimétriques, C. R. acad. sci. Paris, 288, 287-289, (1979) · Zbl 0406.14011
[19] {\scB. Teissier}, Bonnesen-type inequalities in algebraic geometry, I: Introduction to the problem, preprint. · Zbl 0494.52009
[20] Welsh, D.J.A, Matroid theory, (1976), Academic Press London/New York · Zbl 0343.05002
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.