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5 papers · 2 filters
Weighted de Bruijn Graphs for the Menage Problem and Its Generalizations
Max A. Alekseyev
We address the problem of enumeration of seating arrangements of married couples around a circular table such that no spouses sit next to each other and no k consecutive persons ar…
The -invariant and catenary data of a matroid
Joseph E. Bonin, Joseph P. S. Kung
The catenary data of a matroid of rank on elements is the vector , indexed by compositions , where ,\, $a_i…
Lattices related to extensions of presentations of transversal matroids
Joseph E. Bonin
For a presentation of a transversal matroid , we study the set of single-element transversal extensions of that have presentations that exten…
Khovanov-Rozansky homology and Directed Cycles
Hao Wu
We determine the cycle packing number of a directed graph using elementary projective algebraic geometry. Our idea is rooted in the Khovanov-Rozansky theory. In fact, using the Kho…
An infinite family of excluded minors for strong base-orderability
Joseph E. Bonin, Thomas J. Savitsky
We discuss a conjecture of Ingleton on excluded minors for base-orderability, and, extending a result he stated, we prove that infinitely many of the matroids that he identified ar…