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Standard complexes of matroids and lattice paths

  • 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.

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Author:Alexander Engström, Raman SanyalORCiDGND, Christian StumpORCiDGND
URN:urn:nbn:de:hebis:30:3-695824
DOI:https://doi.org/10.1007/s10013-021-00546-z
ISSN:2305-2228
Parent Title (English):Vietnam journal of mathematics
Publisher:Springer
Place of publication:Singapore
Document Type:Article
Language:English
Date of Publication (online):2022/02/10
Date of first Publication:2022/02/10
Publishing Institution:Universitätsbibliothek Johann Christian Senckenberg
Release Date:2023/09/22
Tag:Lattice path matroids; Simplicial complexes; Standard monomials
Volume:50
Issue:3
Page Number:17
First Page:763
Last Page:779
Note:
Supported by DFG grant STU 563/4-1 “Noncrossing phenomena in Algebra and Geometry”.
Note:
Open Access funding enabled and organized by Projekt DEAL.
HeBIS-PPN:513642994
Institutes:Informatik und Mathematik
Dewey Decimal Classification:5 Naturwissenschaften und Mathematik / 51 Mathematik / 510 Mathematik
MSC-Classification:05-XX COMBINATORICS (For finite fields, see 11Txx) / 05Bxx Designs and configurations (For applications of design theory, see 94C30) / 05B35 Matroids, geometric lattices [See also 52B40, 90C27]
05-XX COMBINATORICS (For finite fields, see 11Txx) / 05Exx Algebraic combinatorics
13-XX COMMUTATIVE RINGS AND ALGEBRAS / 13Pxx Computational aspects and applications [See also 14Qxx, 68W30] / 13P25 Applications of commutative algebra (e.g., to statistics, control theory, optimization, etc.)
52-XX CONVEX AND DISCRETE GEOMETRY / 52Bxx Polytopes and polyhedra / 52B40 Matroids (realizations in the context of convex polytopes, convexity in combinatorial structures, etc.) [See also 05B35, 52Cxx]
Sammlungen:Universitätspublikationen
Licence (German):License LogoCreative Commons - CC BY - Namensnennung 4.0 International

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