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A quasi-tree expansion of the Krushkal polynomial
quasi-tree expansion Krushkal polynomial Combinatorics
2012/5/24
We introduce a generalization of the Krushkal polynomial to nonorientable surfaces, and prove that this polynomial has a natural quasi-tree expansion. This generalized Krushkal polynomial contains the...
Abstract: The degree chromatic polynomial $Pm(G,k)$ of a graph $G$ counts the number of $k$-colorings in which no vertex has $m$ adjacent vertices of its same color. We prove Humpert and Martin's conj...
Polynomial realizations of some combinatorial Hopf algebras
Hopf algebras of decorated rooted trees Free quasi-symmetric functions
2010/12/3
We construct explicit polynomial realizations of some combinatorial Hopf algebras based on various kind of trees or forests, and some more general classes of graphs, ranging from the Connes-Kreimer al...
The limiting Kac random polynomial and truncated random orthogonal matrices
limiting Kac random polynomial truncated random orthogonal matrices
2010/12/7
An exact calculation of the eigenvalue statistics of truncated random Haar distributed real orthogonal matrices has recently been carried out by Khoruzhenko, Sommers and Zyczkowski. We further develop...