dc.contributor.author
Benedetti-Velásquez, C.
dc.contributor.author
Knauer, K.
dc.date.accessioned
2024-05-08T13:13:05Z
dc.date.accessioned
2024-09-19T14:25:32Z
dc.date.available
2024-05-08T13:13:05Z
dc.date.available
2024-09-19T14:25:32Z
dc.date.issued
2024-04-04
dc.identifier.uri
http://hdl.handle.net/2072/537580
dc.description.abstract
We characterize the quotients among lattice path matroids (LPMs) in terms of their diagrams. This characterization allows us to show that ordering LPMs by quotients yields a graded poset, whose rank polynomial has the Narayana numbers as coefficients. Furthermore, we study full lattice path flag matroids and show that—contrary to arbitrary positroid flag matroids—they correspond to points in the nonnegative flag variety. At the basis of this result lies an identification of certain intervals of the strong Bruhat order with lattice path flag matroids. A recent conjecture of Mcalmon, Oh, and Xiang states a characterization of quotients of positroids. We use our results to prove this conjecture in the case of LPMs. © The Author(s) 2024.
eng
dc.description.sponsorship
We thank Lauren Williams for insightful conversations and Suho Oh for sharing their conjecture with us. Benedetti was supported by Grant FAPA of the Faculty of Science at Universidad de los Andes. Knauer was supported by the Spanish State Research Agency through Grants RYC-2017-22701, PID2019-104844GB-I00 and the Severo Ochoa and Mar\u00EDa de Maeztu Program for Centers and Units of Excellence in R &D (CEX2020-001084-M). We also thank the CIMPA-ICTP Research In Pairs program.
dc.format.extent
30 p.
cat
dc.publisher
Springer Science and Business Media Deutschland GmbH
cat
dc.relation.ispartof
Combinatorica
cat
dc.rights
L'accés als continguts d'aquest document queda condicionat a l'acceptació de les condicions d'ús establertes per la següent llicència Creative Commons: https://creativecommons.org/licenses/by/4.0/
dc.source
RECERCAT (Dipòsit de la Recerca de Catalunya)
dc.subject.other
Flag matroids; Lattice path matroids; Quotients
cat
dc.title
Lattice Path Matroids and Quotients
cat
dc.type
info:eu-repo/semantics/article
cat
dc.type
info:eu-repo/semantics/publishedVersion
cat
dc.identifier.doi
10.1007/s00493-024-00085-4
cat
dc.rights.accessLevel
info:eu-repo/semantics/openAccess
