×

Majorization on finite partially ordered sets. (English) Zbl 0503.06001


MSC:

06A06 Partial orders, general
26D20 Other analytical inequalities
PDFBibTeX XMLCite
Full Text: DOI

References:

[1] Ahlswede, Rudolf; Daykin, DavidE., An inequality for the weights of two families of sets, their unions and intersections, Z. Wahrsch. Verw. Gebiete, 43, 183, (1978) · Zbl 0357.04011
[2] Ahlswede, Rudolf; Daykin, DavidE., Inequalities for a pair of maps \(S× S→ S\) with {\it S} a finite set, Math. Z., 165, 267, (1979) · Zbl 0424.05005
[3] Chung, F. R. K.; Hwang, F. K., On blocking probabilities for a class of linear graphs, Bell System Tech. J., 57, 2915, (1978) · Zbl 0389.94023
[4] Fortuin, C. M.; Kasteleyn, P. W.; Ginibre, J., Correlation inequalities on some partially ordered sets, Comm. Math. Phys., 22, 89, (1971) · Zbl 0346.06011
[5] Hardy, G. H.; Littlewood, J. E.; Pólya, G., Inequalities, (1959) · JFM 60.0169.01
[6] Holley, Richard, Remarks on the \({\rm FKG}\) inequalities, Comm. Math. Phys., 36, 227, (1974)
[7] Hwang, F. K., Majorization on a partially ordered set, Proc. Amer. Math. Soc., 76, 199, (1979) · Zbl 0449.06001
[8] Hwang, F. K., Generalized Huffman trees, SIAM J. Appl. Math., 37, 124, (1979) · Zbl 0409.05028 · doi:10.1137/0137008
[9] Hwang, F. K., Generalized Schur functions, Bull. Inst. Math. Acad. Sinica, 8, 513, (1980)
[10] Kemperman, J. H. B., On the FKG-inequality for measures on a partially ordered space, Nederl. Akad. Wetensch. Proc. Ser. A 80=Indag. Math., 39, 313, (1977) · Zbl 0384.28012
[11] Marshall, AlbertW.; Olkin, Ingram, Inequalities: theory of majorization and its applications, (1979) · Zbl 0437.26007
[12] Muirhead, R. F., Some methods applicable to identities and inequalities of symmetric algebraic functions of {\it n} letters, Proc. Edinburgh Math. Soc., 21, 144, (1903) · JFM 34.0202.01
[13] Ostrowski, P. A., Sur quelques applications des fonctions convexes et concaves au sens de I. Schur, J. Math. Pures Appl. (9), 31, 253, (1952) · Zbl 0047.29602
[14] Preston, C. J., A generalization of the \({\rm FKG}\) inequalities, Comm. Math. Phys., 36, 233, (1974)
[15] Schur, I., Über ein klasse von mittelbildungen mit anwendungen auf die determinantetheorie, Sitzungsber. Berlin. Math. Ges., 22, 9, (1923) · JFM 49.0054.01
[16] Seymour, P. D.; Welsh, D. J. A., Combinatorial applications of an inequality from statistical mechanics, Math. Proc. Cambridge Philos. Soc., 77, 485, (1975) · Zbl 0345.05004
[17] Shapley, LloydS., Cores of convex games, Internat. J. Game Theory, 1, (197172) · Zbl 0222.90054
[18] Shepp, L. A., The FKG inequality and some monotonicity properties of partial orders, SIAM J. Algebraic Discrete Methods, 1, 295, (1980) · Zbl 0501.06006
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. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.