The aim of this note is to give some factorisation formulas for different versions of the Macdonald polynomials when the parameter t is specialized at roots of unity, generalizing...
We provide a new proof of Brylawski’s formula for the Tutte polynomial of the tensor product of two matroids. Our proof involves extending Tutte’s formula, expressing the Tutte...
Let Φ be a uniformly distributed random k-SAT formula with n variables and m clauses. We prove that the Walksat algorithm from [16, 17] finds a satisfying assignment of Φ in pol...
We say that a polynomial f(x1, . . . , xn) is indecomposable if it cannot be written as a product of two polynomials that are defined over disjoint sets of variables. The polynom...
It is shown that the Hilbert series of the face ring of a clique complex (equivalently, flag complex) of a graph G is, up to a factor, just a specialization of SG (x, y), the subg...