A Generalized Macaulay Theorem and Generalized Face Rings

dc.creatorNevo, Eran
dc.date2005-05-16
dc.date2006-02-23
dc.date.accessioned2026-07-07T06:39:57Z
dc.date.available2026-07-07T06:39:57Z
dc.descriptionWe prove that the $f$-vector of members in a certain class of meet semi-lattices satisfies Macaulay inequalities. We construct a large family of meet semi-lattices belonging to this class, which includes all posets of multicomplexes, as well as meet semi-lattices with the "diamond property", discussed by Wegner, as spacial cases. Specializing the proof to that later family, one obtains the Kruskal-Katona inequalities and their proof as in Wegner's. For geometric meet semi lattices we construct an analogue of the exterior face ring, generalizing the classic construction for simplicial complexes. For a more general class, which include also multicomplexes, we construct an analogue of the Stanley-Reisner ring. These two constructions provide algebraic counterparts (and thus also algebraic proofs) of Kruskal-Katona's and Macaulay's inequalities for these classes, respectively.
dc.descriptionFinal version: 13 pages, 2 figures. Improved presentation, more detailed proofs, same results. To appear in JCTA
dc.identifierhttps://arxiv.org/abs/math/0505330
dc.identifierhttp://arxiv.org/abs/math/0505330
dc.identifierJCTA 113 (2006) 1321-1331
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/101274
dc.subjectCombinatorics
dc.subject06A12; 13F55
dc.titleA Generalized Macaulay Theorem and Generalized Face Rings
dc.typetext

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