Related papers: Counting Parabolic Double Cosets in Symmetric Grou…
Initiated by Davis, Nelson, Petersen and Tenner (2018), the enumerative study of pinnacle sets of permutations has attracted a fair amount of attention recently. In this article, we provide a recurrence that can be used to compute…
We provide a sharp estimate for the asymptotic number of lattice zonotopes, inscribed in $[0,n ]^d$ when $n$ tends to infinity. Our estimate refines the logarithmic equivalent established by Barany, Bureaux, and Lund when the sum of the…
We establish the solvability of second order divergence type parabolic systems in Sobolev spaces. The leading coefficients are assumed to be only measurable in one spatial direction on each small parabolic cylinder with the spatial…
We completely describe the algebraic part of the rational cohomology of the Torelli groups of the manifolds $\#^g S^n \times S^n$ relative to a disc in a stable range, for $2n \geq 6$. Our calculation is also valid for $2n=2$ assuming that…
We describe an algorithm for counting points on an arbitrary hyperelliptic curve over a finite field of odd characteristic, using Monsky-Washnitzer cohomology to compute a p-adic approximation to the characteristic polynomial of Frobenius.…
Quickly convergent series are given to compute polyzeta numbers. The formula involves an intricate combination of (generalized) polylogarithms at 1/2. However, the combinatorics has a very simple geometric interpretation: it corresponds…
Corner trees, introduced in "Even-Zohar and Leng, 2021, Proceedings of the 2021 ACM-SIAM Symposium on Discrete Algorithms", allow for the efficient counting of certain permutation patterns. Here we identify corner trees as a subset of…
This paper continues the study initiated in [B. Davey, Parabolic theory as a high-dimensional limit of elliptic theory, Arch Rational Mech Anal 228 (2018)], where a high-dimensional limiting technique was developed and used to prove certain…
Let A be a nonempty finite set of relatively prime positive integers, and let p_A(n) denote the number of partitions of n with parts in A. An elementary arithmetic argument is used to obtain an asymptotic formula for p_A(n).
We review the coset construction of conformal field theories; the emphasis is on the construction of the Hilbert spaces for these models, especially if fixed points occur. This is applied to the $N=2$ superconformal cosets constructed by…
We continue the study of the retraction from an Artin group to a standard parabolic subgroup introduced by Blufstein, Charney, Paris and the second author. Using right and left retractions we obtain new results on minimal parabolic…
In this paper, we state two combination theorems for relatively quasiconvex subgroups in a relatively hyperbolic group. Applications are given to the separability of double cosets of certain relatively quasiconvex subgroups and the…
The concept of S-permutation matrix is considered. A general formula for counting all disjoint pairs of $n^2 \times n^2$ S-permutation matrices as a function of the positive integer $n$ is formulated and proven in this paper. To do that,…
For right-angled Coxeter groups $W_{\Gamma}$, we obtain a condition on $\Gamma$ that is necessary and sufficient to ensure that $W_{\Gamma}$ is thick and thus not relatively hyperbolic. We show that Coxeter groups which are not thick all…
Let q be a power of a prime and n a positive integer. Let P(q) be a parabolic subgroup of the finite general linear group GL(n,q). We show that the number of P(q)-conjugacy classes in GL(n,q) is, as a function of q, a polynomial in q with…
After classifying 3-dimensional hyperbolic Coxeter pyramids by means of elementary plane geometry, we calculate growth functions of corresponding Coxeter groups by using Steinberg formula and conclude that growth rates of them are always…
We develop the relationship between quaternionic hyperbolic geometry and arithmetic counting or equidistribution applications, that arises from the action of arithmetic groups on quaternionic hyperbolic spaces, especially in dimension $2$.…
We develop further in this work the high order paracontrolled calculus setting to deal with the analytic part of the study of quasilinear singular PDEs. A number of continuity results for some operators are proved for that purpose. Unlike…
We enlarge a Coxeter group into a category, with one object for each finite parabolic subgroup, encoding the combinatorics of double cosets. This category, the singular Coxeter monoid, is connected to the geometry of partial flag varieties.…
We characterize the double centralizer of all parabolic subgroups of the braid groups. We apply this result to provide a new and potentially more efficient solution to the subgroup conjugacy problem for parabolic subgroups. In the course of…