We present two splitting formulas for calculating the Tutte polynomial of a matroid. The first one is for a generalized parallel connection across a 3-point line of two matroids and the second one is applicable to a 3-sum of two matroids. An important tool used is the bipointed Tutte polynomial of a
A Convolution Formula for the Tutte Polynomial
โ Scribed by W. Kook; V. Reiner; D. Stanton
- Publisher
- Elsevier Science
- Year
- 1999
- Tongue
- English
- Weight
- 75 KB
- Volume
- 76
- Category
- Article
- ISSN
- 0095-8956
No coin nor oath required. For personal study only.
โฆ Synopsis
Following Crapo [2], let `(x, y)(M)=x r(M) y r(M*) , where K=Z[x, y].
Lemma 1. (x, y) &1 =(&x, &y).
๐ SIMILAR VOLUMES
For any matroid M realizable over Q , we give a combinatorial interpretation of the Tutte polynomial T M (x, y) which generalizes many of its known interpretations and specializations, including Tutte's coloring and flow interpretations of T M (1t, 0), T M (0, 1t); Crapo and Rota's finite field inte
We present formulas of Rodrigues type giving the Macdonald polynomials for arbitrary partitions \* through the repeated application of creation operators B k , k=1, ..., l (\*) on the constant 1. Three expressions for the creation operators are derived one from the other. When the last of these expr
Communicated by B
## Abstract We prove a Capelli type theorem on the canonical decomposition for multiplicative convolutions of polynomials. We derive then some irreducibility criteria for convolutions of polynomials in several variables over a given field. The irreducibility conditions are expressed only in terms o