Symmetric edge polytopes and matching generating polynomials

Polynomials and Polytopes

At first sight solutions to systems of polynomial equations and convex polytopes do not seem to be related at all. However, there is a very direct connection between the two. Newton pioneered the study, but it was in recent years that many important (and fascinating) results have been discovered. Bernd Sturmfels presents one such result and provides an algorithmic proof in [7]. It suggests an a...

On edge detour index polynomials

The edge detour index polynomials were recently introduced for computing the edge detour indices. In this paper we find relations among edge detour polynomials for the 2-dimensional graph of $TUC_4C_8(S)$ in a Euclidean plane and $TUC4C8(S)$ nanotorus.

Decomposition of Polytopes and Polynomials

Motivated by a connection with the factorization of multivariable polynomials, we study integral convex polytopes and their integral decompositions in the sense of the Minkowski sum. We first show that deciding decomposability of integral polygons is NP-complete then present a pseudo-polynomial time algorithm for decomposing polygons. For higher dimensional polytopes, we give a heuristic algori...

Tutte polynomials of wheels via generating functions

We find an explicit expression of the Tutte polynomial of an $n$-fan. We also find a formula of the Tutte polynomial of an $n$-wheel in terms of the Tutte polynomial of $n$-fans. Finally, we give an alternative expression of the Tutte polynomial of an $n$-wheel and then prove the explicit formula for the Tutte polynomial of an $n$-wheel.

Srikumar 1 Perfect Matching and Matching Polytopes