30 research outputs found
Polytopes associated to Dihedral Groups
In this note we investigate the convex hull of those -permutation
matrices that correspond to symmetries of a regular -gon. We give the
complete facet description. As an application, we show that this yields a
Gorenstein polytope, and we determine the Ehrhart -vector
Enumerative properties of Ferrers graphs
We define a class of bipartite graphs that correspond naturally with Ferrers
diagrams. We give expressions for the number of spanning trees, the number of
Hamiltonian paths when applicable, the chromatic polynomial, and the chromatic
symmetric function. We show that the linear coefficient of the chromatic
polynomial is given by the excedance set statistic.Comment: 12 page
Stability of Kronecker coefficients via discrete tomography
In this paper we give a new sufficient condition for a general stability of
Kronecker coefficients, which we call it additive stability. It was motivated
by a recent talk of J. Stembridge at the conference in honor of Richard P.
Stanley's 70th birthday, and it is based on work of the author on discrete
tomography along the years. The main contribution of this paper is the
discovery of the connection between additivity of integer matrices and
stability of Kronecker coefficients. Additivity, in our context, is a concept
from discrete tomography. Its advantage is that it is very easy to produce lots
of examples of additive matrices and therefore of new instances of stability
properties. We also show that Stembridge's hypothesis and additivity are
closely related, and prove that all stability properties of Kronecker
coefficients discovered before fit into additive stability.Comment: 22 page