Decomposing Bj\"orner's Matrix
\'Swiatos{\l}aw R. GaL
TL;DR
This paper provides an alternative proof for Bj"orner's conjecture that a certain matrix relating face numbers and g numbers of polytopes is totally non-negative, with some discussion on simple flag polytopes.
Contribution
It offers a new proof of Bj"orner's conjecture and explores implications for simple flag polytopes.
Findings
Matrix is totally non-negative as conjectured
Provides an alternative proof of Bj"orner's conjecture
Discusses implications for simple flag polytopes
Abstract
We give an alternative proof of a (former) conjecture of Bj\"orner stating that the matrix expressing face numbers in terms of g numbers is totally non-negative. We briefly discuss the case of simple flag polytopes.
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Taxonomy
TopicsAdvanced Combinatorial Mathematics · Advanced Mathematical Theories and Applications