P-flag spaces and incidence stratifications

Bolognini, Davide; Sentinelli, Paolo

doi:10.1007/s00029-021-00685-8

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Cited by 2 publications

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“…Coxeter matroids generalize, via the maximality property, standard matroids. By extending maximality property to different contexts, in [8] we generalized flag matroids to

P

‐flag matroids and in [9] matroids to

\chi

‐matroids, where

P

is any finite poset and

\chi

a one‐dimensional character of a finite group. In this paper, we provide another connection between matroids and Coxeter matroids involving barycentric subdivisions of simplicial complexes (Theorem 4.1).…”

Section: Introductionmentioning

confidence: 99%

Linear extensions and shelling orders

Bolognini

Sentinelli

2023

Bulletin of London Math Soc

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We prove that linear extensions of the Bruhat order of a matroid are shelling orders and that the barycentric subdivision of a matroid is a Coxeter matroid, viewing barycentric subdivisions as subsets of a parabolic quotient of a symmetric group. A similar result holds for order ideals in minuscule quotients of symmetric groups and in their barycentric subdivisions. Moreover, we apply promotion and evacuation for labeled graphs of Malvenuto and Reutenauer to dual graphs of simplicial complexes, introducing promotion and evacuation of shelling orders.

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“…Coxeter matroids generalize, via the maximality property, standard matroids. By extending maximality property to different contexts, in [8] we generalized flag matroids to