solidot新版网站常见问题,请点击这里查看。
消息
本文已被查看3714次
Hopf algebras and Tutte polynomials. (arXiv:1508.00814v3 [math.CO] UPDATED)
来源于:arXiv
By considering Tutte polynomials of Hopf algebras, we show how a Tutte
polynomial can be canonically associated with combinatorial objects that have
some notions of deletion and contraction. We show that several graph
polynomials from the literature arise from this framework. These polynomials
include the classical Tutte polynomial of graphs and matroids, Las Vergnas'
Tutte polynomial of the morphism of matroids and his Tutte polynomial for
embedded graphs, Bollobas and Riordan's ribbon graph polynomial, the Krushkal
polynomial, and the Penrose polynomial.
We show that our Tutte polynomials of Hopf algebras share common properties
with the classical Tutte polynomial, including deletion-contraction
definitions, universality properties, convolution formulas, and duality
relations. New results for graph polynomials from the literature are then
obtained as examples of the general results.
Our results offer a framework for the study of the Tutte polynomial and its
analogues in other setting 查看全文>>