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
$(q1)^{n+1} q^{\frac{(n+1)(n2)}{2}}\sum_\theta q^{inv(\theta)}$,
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 
