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Scientific article
English

Log-concavity and compressed ideals in certain Macaulay posets

Published inDiscrete mathematics, vol. 254, no. 1-3, p. 421-432
Publication date2002
Abstract

Let Bn be the poset of subsets of {1; 2; : : : ; n} ordered byinclusion and Mn be the poset of monomials in x1; x2; : : : ; xn ordered bydivisibility. Both these posets have an additional linear order making them what is called Macaulayposets. We show in this paper that the pro-les (also called f-vectors) of ideals in Bn and Mn generated bythe -rst elements (relativelyto the linear order) of a given rank are log-concave.

Keywords
  • Log-concavity
  • Binomial coe1cients
  • Macaulay posets
  • Unimodality
Citation (ISO format)
PITTELOUD, Philippe. Log-concavity and compressed ideals in certain Macaulay posets. In: Discrete mathematics, 2002, vol. 254, n° 1-3, p. 421–432. doi: 10.1016/S0012-365X(01)00360-0
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ISSN of the journal0012-365X
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