Whitney numbers of matroid extensions and co-extensions

Whitney numbers of matroid extensions and co-extensions

Crapo found that single-element extensions of matroid are equivalent to modular cuts. This paper will study the single-element extension and co-extension of a matroid and establish the upper semi-continuity for the signless coefficients of Whitney polynomials and Whitney numbers on both extensions v...

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Veröffentlicht in:Discrete mathematics 2023-01, Vol.346 (1), p.113131, Article 113131
Hauptverfasser: Fu, Houshan, Wang, Suijie
Format: Artikel
Sprache:eng
Schlagworte:
Extension lattice
Single-element extension
Whitney number
Whitney polynomial
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Beschreibung
Zusammenfassung:Crapo found that single-element extensions of matroid are equivalent to modular cuts. This paper will study the single-element extension and co-extension of a matroid and establish the upper semi-continuity for the signless coefficients of Whitney polynomials and Whitney numbers on both extensions via its extension lattice, a lattice of all non-empty modular cuts.
ISSN:0012-365X
1872-681X
DOI:10.1016/j.disc.2022.113131