An Inequality for Kruskal-macaulay Functions
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چکیده
for some N ≥ k + 1, then the equality in (1.2) occurs only when a = 0. Kruskal-Macaulay functions are relevant for their applications to the study of antichains in multisets (see for example [11, 2]), posets, rings and polyhedral combinatorics (see [5] and the survey [3]). In particular, they play and important role in proving results, extensions and generalizations of classical problems concerning the Kruskal-Katona [12, 10, 15], Macaulay [13], and Erdős-Ko-Rado [9] theorems. More recently, the authors [1], applied Theorem 1 to the problem of finding the maximum number of translated copies of a pattern that can
منابع مشابه
Results on Generalization of Burch’s Inequality and the Depth of Rees Algebra and Associated Graded Rings of an Ideal with Respect to a Cohen-Macaulay Module
Let be a local Cohen-Macaulay ring with infinite residue field, an Cohen - Macaulay module and an ideal of Consider and , respectively, the Rees Algebra and associated graded ring of , and denote by the analytic spread of Burch’s inequality says that and equality holds if is Cohen-Macaulay. Thus, in that case one can compute the depth of associated graded ring of as In this paper we ...
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