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10 papers · 2 filters
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…
The densest matroids in minor-closed classes with exponential growth rate
Jim Geelen, Peter Nelson
The for a nonempty minor-closed class of matroids is the function whose value at an integer is define…
A pattern avoidance criterion for free inversion arrangements
William Slofstra
We show that the hyperplane arrangement of a coconvex set in a finite root system is free if and only if it is free in corank 4. As a consequence, we show that the inversion arrang…
On the Minimum Edge-Density of 4-Critical Graphs of Girth Five
Chun-Hung Liu, Luke Postle
We prove that if G is a 4-critical graph of girth at least five then |E(G)|>=(5|V(G)|+2)/3. As a corollary, graphs of girth at least five embeddable in the Klein bottle or torus ar…
Erdős-Ko-Rado for Perfect Matchings
Nathan Lindzey
A perfect matching of a complete graph is a 1-regular subgraph that contains all the vertices. Two perfect matchings intersect if they share an edge. It is known that if $…
On the Smallest Eigenvalue of Grounded Laplacian Matrices
Mohammad Pirani, Shreyas Sundaram
We provide upper and lower bounds on the smallest eigenvalue of grounded Laplacian matrices (which are matrices obtained by removing certain rows and columns of the Laplacian matri…