Tropical geometry of Rado matroids | [Discrete Mathematics Letters • 2024]

Author(s):

1. Calum Buchanan: Department of Mathematics & Statistics, University of Vermont,Burlington, VT,USA

2. Richard Danner: Department of Mathematics & Statistics, University of Vermont,Burlington, VT,USA

Abstract:

In this article, we characterize the products of simplicial generators for the Chow ring of a loopless matroid, extending a result of Backman, Eur, and Simpson [J. Eur. Math. Soc., DOI: 10.4171/JEMS/1350]. We prove that the stable intersection of a collection of tropical hyperplanes centered at the origin with the Bergman fan of a matroid is the Bergman fan of the dual of a certain Rado matroid.

Page(s): 27-30

DOI: 10.47443/dml.2024.044

Published: Journal: Discrete Mathematics Letters, Volume: 14, Issue: 0, Year: 2024

Keywords:

tropical geometry , Chow ring , Rado matroid

References:

[1] Adiprasito K.,Huh J.,E. Katz. J.,Backman S.,Eur C.,Simpson C.,C. De Concini C.,Procesi C.,Eur C.,Larson M.,Feichtner E. M.,Yuzvinsky S.,Fink A.,Olarte J. A.,Hampe S.,Larson M.,Larson M.,Li S.,Payne S.,Proudfoot N.,Nash-Williams C. S. J. A.,Rado R. .1942 .A theorem on independence relations, Q. J. Combin. Theory Ser. B, 13(1) : 83-89.

[2] Speyer D. E.,Yuzvinsky S. .2002 .Small rational model of subspace complement. Trans. Amer. Math. Soc, 354(5) : 1921-1945.

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