Standard Complexes of Matroids and Lattice Paths

Alexander Engström; Raman Sanyal; Christian Stump

doi:10.1007/s10013-021-00546-z

Standard Complexes of Matroids and Lattice Paths

Alexander Engström, Raman Sanyal^*, Christian Stump

^*Corresponding author for this work

Department of Mathematics and Systems Analysis

Research output: Contribution to journal › Article › Scientific › peer-review

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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.

Original language	English
Pages (from-to)	763-779
Number of pages	17
Journal	Vietnam Journal of Mathematics
Volume	50
Issue number	3
Early online date	10 Feb 2022
DOIs	https://doi.org/10.1007/s10013-021-00546-z
Publication status	Published - Jul 2022
MoE publication type	A1 Journal article-refereed

Funding

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.

Keywords

Lattice path matroids
Simplicial complexes
Standard monomials

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10.1007/s10013-021-00546-zLicence: CC BY

Standard Complexes of Matroids and Lattice PathsFinal published version, 1.06 MBLicence: CC BY

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title = "Standard Complexes of Matroids and Lattice Paths",

abstract = "Motivated by Gr{\"o}bner 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.",

keywords = "Lattice path matroids, Simplicial complexes, Standard monomials",

author = "Alexander Engstr{\"o}m and Raman Sanyal and Christian Stump",

note = "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 Universit{\"a}t Berlin when the authors collaborated over the summer at the “villa” of the Discrete Geometry Group. Publisher Copyright: {\textcopyright} 2022, The Author(s).",

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language = "English",

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T1 - Standard Complexes of Matroids and Lattice Paths

AU - Engström, Alexander

AU - Sanyal, Raman

AU - Stump, Christian

N1 - 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).

PY - 2022/7

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N2 - 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.

AB - 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.

KW - Lattice path matroids

KW - Simplicial complexes

KW - Standard monomials

UR - https://www.scopus.com/pages/publications/85127401790

U2 - 10.1007/s10013-021-00546-z

DO - 10.1007/s10013-021-00546-z

M3 - Article

AN - SCOPUS:85127401790

SN - 2305-221X

VL - 50

SP - 763

EP - 779

JO - Vietnam Journal of Mathematics

JF - Vietnam Journal of Mathematics

IS - 3

ER -

Standard Complexes of Matroids and Lattice Paths

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