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
Closed Product Formulas for CertainR-polynomials
โ Scribed by Mario Marietti
- Publisher
- Elsevier Science
- Year
- 2002
- Tongue
- English
- Weight
- 70 KB
- Volume
- 23
- Category
- Article
- ISSN
- 0195-6698
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โฆ Synopsis
R-polynomials get their importance from the fact that they are used to define and compute the Kazhdan-Lusztig polynomials, which have applications in several fields. Here we give a closed product formula for certain R-polynomials valid for every Coxeter group. This result implies a conjecture due to F. Brenti about the symmetric groups.
๐ SIMILAR VOLUMES
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
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).