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arXiv · 2306.01947

Bipartite Determinantal Ideals and concurrent vertex maps

Li Li
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Abstract

Bipartite determinantal ideals are introduced by Illian and the author as a vast generalization of the classical determinantal ideals intensively studied in commutative algebra, algebraic geometry, representation theory and combinatorics. We introduce a combinatorial model called concurrent vertex maps to describe the Stanley-Reisner complex of the initial ideal of any bipartite determinantal ideal, and study properties and applications of this model including vertex decomposability, shelling orders, formulas of the Hilbert series and $h$-polynomials.

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Li Li. 2023-06-02. Bipartite Determinantal Ideals and concurrent vertex maps. https://arxiv.org/abs/2306.01947

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