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Combinatorial theory of flag arrangements

Published on:

2 April 2024

Primary Category:

Combinatorics

Paper Authors:

Omid Amini,

Lucas Gierczak

Bullets

Key Details

Matricubes axiomatize arrangements of initial flags in vector spaces

Equivalent axiomatic systems are given involving rank functions, flats, circuits, and independent sets

Matricubes generalize matroid theory

Links are made to permutation arrays and coherent complexes of matroids

Many open questions and research directions are discussed

AI generated summary

Combinatorial theory of flag arrangements

This paper introduces matricubes, combinatorial objects that generalize matroid theory and provide an axiomatization of arrangements of initial flags in a vector space. The authors give several equivalent cryptomorphic axiomatic systems for matricubes in terms of rank functions, flats, circuits, and independent sets. Connections are made to permutation arrays and coherent complexes of matroids. Open questions are raised about bases, representability, Tutte polynomials, and a stratification of products of flag varieties.

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