We generalize the definition and enumeration of spanning trees from the setting of graphs to
that of arbitrary-dimensional simplicial complexes $\Delta $, extending an idea due to G …

The graph algebra is a commutative, cocommutative, graded, connected incidence Hopf
algebra, whose basis elements correspond to finite graphs, and whose Hopf product and …

Much information about a graph can be obtained by studying its spanning trees. On the
other hand, a graph can be regarded as a 1-dimensional cell complex, raising the question …

The Tutte polynomial of a graph or a matroid, named after WT Tutte, has the important
universal property that essentially any multiplicative graph or network invariant with a …

In this paper, we study flag structures of matroid base polytopes. We describe faces of
matroid base polytopes in terms of matroid data, and give conditions for hyperplane splits of …

The cyclotomic polynomial topologically Page 1 J. reine angew. Math. 687 (2014), 113–132
Journal für die reine und angewandte Mathematik DOI 10.1515/crelle-2012-0051 © De Gruyter …

A Smarandache k-orientation of G for an integer k≥ 0 is such an orientation on G with
exactly k oriented cycles. If k= 0, then it is the common acyclic orientation. In C. Merino and …

We undertake a combinatorial study of the piecewise linear map g: R^{2m+ 2n}--> R^{mn}
which assigns to the four vectors a, A in R^ m and b, B in R^ n the m by n matrix given by g …

In this paper we study monomial cycles in Koszul homology over a monomial ring. The main
result is that a monomial cycle is a boundary precisely when the monomial representing that …

The lacking polynomial is a graph polynomial introduced by Chan, Marckert, and Selig in
2013 that is closely related to the Tutte polynomial of a graph. It arose by way of a …