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12 papers · 2 filters
A general notion of activity for the Tutte polynomial
Julien Courtiel
In the literature can be found several descriptions of the Tutte polynomial of graphs. Tutte defined it thanks to a notion of activity based on an ordering of the edges. Thereafter…
A Baxter class of a different kind, and other bijective results using tableau sequences ending with a row shape
Sophie Burrill, Stephen Melczer, Marni Mishna
Tableau sequences of bounded height have been central to the analysis of k-noncrossing set partitions and matchings. We show here that familes of sequences that end with a row shap…
On Hilbert bases of cuts
Luis Goddyn, Tony Huynh, Tanmay Deshpande
A Hilbert basis is a set of vectors X such that the integer cone (semigroup) generated by X is the intersection of the lattice generated by X with the cone generated by X. Define a…
Interval minors of complete bipartite graphs
Bojan Mohar, Arash Rafiey, Behruz Tayfeh-Rezaie +1
Interval minors of bipartite graphs were recently introduced by Jacob Fox in the study of Stanley-Wilf limits. We investigate the maximum number of edges in -interval mino…
Constructions of complex equiangular lines from mutually unbiased bases
Jonathan Jedwab, Amy Wiebe
A set of vectors of equal norm in represents equiangular lines if the magnitudes of the Hermitian inner product of every pair of distinct vectors in the set are equa…
Graphical representations of graphic frame matroids
Rong Chen, Matt DeVos, Daryl Funk +1
A frame matroid M is graphic if there is a graph G with cycle matroid isomorphic to M. In general, if there is one such graph, there will be many. Zaslavsky has shown that frame ma…