What can be said about pure O-sequences?
type: Item
instance of: scholarly article
title: What can be said about pure O-sequences?
zbMATH Open document ID: 0667.05004
DOI: 10.1016/0097-3165(89)90025-3
author: Takayuki Hibi
published in: Journal of Combinatorial Theory. Series A
publication date: 1989-01-01T00:00:00Z
review text: Let \(f(\Delta)=(f_ 0,f_ 1,...,f_{d-1})\) be the f-vector of a Cohen- Macaulay complex \(\Delta\). Björner proved that (*) \(f_ i\leq f_{(d- 2)-i}\) for any \(0\leq i<[d/2]\) and \((**)\quad f_ 0\leq f_ 1\leq...\leq f_{[(d-1)/2]}.\) Recently, Stanley generalized Björner's inequalities (*) and (**) for pure simplicial complexes. In this paper we consider O- sequence analogue of the inequalities (*) and (**). Let \((h_ 0,h_ 1,...,h_ s),\quad h_ s\neq 0,\) is a pure O-sequence. We shall prove that \(h_ i\leq h_{s-i}\) for any \(0\leq i\leq [s/2]\) and \(h_ 0\leq h_ 1\leq...\leq h_{[(s+1)/2]}.\)
Mathematics Subject Classification ID: 05A15
zbMATH DE Number: 4091512
zbMATH Keywords: sequences
zbMATH Keywords: Cohen-Macaulay complex
MaRDI profile type: Publication
full work available at URL: 0097-3165(89)90025-3
OpenAlex ID: W2004918406
cites work: Q3741626
cites work: Q5805073
cites work: Q4196436
cites work: Q4153339
cites work: Hilbert functions of graded algebras
cites work: Combinatorics and commutative algebra.
description: scientific article; zbMATH DE number 4091512