TY - JOUR
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
Y1 - 2022/7
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 - http://www.scopus.com/inward/record.url?scp=85127401790&partnerID=8YFLogxK
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 -