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Search: MSC category 05A19 ( Combinatorial identities, bijective combinatorics )

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1. CJM 2016 (vol 68 pp. 481)

Bacher, Roland; Reutenauer, Christophe
Number of Right Ideals and a $q$-analogue of Indecomposable Permutations
We prove that the number of right ideals of codimension $n$ in the algebra of noncommutative Laurent polynomials in two variables over the finite field $\mathbb F_q$ is equal to $(q-1)^{n+1} q^{\frac{(n+1)(n-2)}{2}}\sum_\theta q^{inv(\theta)}$, where the sum is over all indecomposable permutations in $S_{n+1}$ and where $inv(\theta)$ stands for the number of inversions of $\theta$.

Keywords:permutation, indecomposable permutation, subgroups of free groups
Categories:05A15, 05A19

2. CJM 2002 (vol 54 pp. 1086)

Polterovich, Iosif
Combinatorics of the Heat Trace on Spheres
We present a concise explicit expression for the heat trace coefficients of spheres. Our formulas yield certain combinatorial identities which are proved following ideas of D.~Zeilberger. In particular, these identities allow to recover in a surprising way some known formulas for the heat trace asymptotics. Our approach is based on a method for computation of heat invariants developed in [P].

Categories:05A19, 58J35

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