On the flag f-vector of a graded lattice with nontrivial homology

2010/12/07 by Christos A. Athanasiadis, Athanasiadis, Christos A.
Mathematics · #06A11 #Advanced Combinatorial Mathematics #Algebraic structures and combinatorial models #Combinatorics (math.CO) #Commutative Algebra and Its Applications #FOS: Mathematics #math.CO #msc:06A11

paper · pdf · doi:10.48550/arxiv.1012.1451

Conjectures 1.4 and 1.5 were disproved by Sam Kolins and have been removed. Conjecture 1.3 remains open

openalex publication_date 2010/12/07 · arxiv created 2011/05/14 · arxiv updated 2011/05/17 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

It is proved that the Boolean algebra of rank n minimizes the flag f-vector among all graded lattices of rank n, whose proper part has nontrivial top-dimensional homology. The analogous statement for the flag h-vector is conjectured in the Cohen-Macaulay case.

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