Standard Complexes of Matroids and Lattice Paths

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Journal Title
Journal ISSN
Volume Title
A1 Alkuperäisartikkeli tieteellisessä aikakauslehdessä
Date
2022-07
Major/Subject
Mcode
Degree programme
Language
en
Pages
17
763-779
Series
Vietnam Journal of Mathematics, Volume 50, issue 3
Abstract
Motivated by Gröbner basis theory for finite point configurations, we define and study the class of standard complexes associated to a matroid. Standard complexes are certain subcomplexes of the independence complex that are invariant under matroid duality. For the lexicographic term order, the standard complexes satisfy a deletion-contraction-type recurrence. We explicitly determine the lexicographic standard complexes for lattice path matroids using classical bijective combinatorics.
Description
Funding Information: Supported by DFG grant STU 563/4-1 “Noncrossing phenomena in Algebra and Geometry”. This project was initiated in 2016 at the Mathematical Institute of Freie Universität Berlin when the authors collaborated over the summer at the “villa” of the Discrete Geometry Group. Publisher Copyright: © 2022, The Author(s).
Keywords
Lattice path matroids, Simplicial complexes, Standard monomials
Other note
Citation
Engström , A , Sanyal , R & Stump , C 2022 , ' Standard Complexes of Matroids and Lattice Paths ' , Vietnam Journal of Mathematics , vol. 50 , no. 3 , pp. 763-779 . https://doi.org/10.1007/s10013-021-00546-z