Related papers: An Inversion Statistic on the Hyperoctahedral Grou…
Collaboration between different data centers is often challenged by heterogeneity across sites. To account for the heterogeneity, the state-of-the-art method is to re-weight the covariate distributions in each site to match the distribution…
In this paper we study the inverse of so-called unfair permutations, and explore various properties of them. Our investigation begins with comparing this class of permutations with uniformly random permutations, and showing that they behave…
The full description of the stable factor-representations of the infinite hyperoctahedral group up to quasi-equivalence obtained.
We introduce the class of partially invertible modules and show that it is an inverse category which we call the Picard inverse category. We use this category to generalize the classical construction of crossed products to, what we call,…
In this paper, an exact bitwise MAP (Maximum A Posteriori) estimation algorithm for group testing problems is presented. We assume a simplest non-adaptive group testing scenario including N-objects with binary status and M-disjunctive…
We present a new probabilistic model of compact commutative Lie groups that produces invariant-equivariant and disentangled representations of data. To define the notion of disentangling, we borrow a fundamental principle from physics that…
Tracking on the rotation group is a key component of many modern systems for estimation of the motion of rigid bodies. To address this problem, here we describe a Bayesian algorithm that relies on directional measurements for tracking on…
For each positive integer $k$ we present an example of Coxeter system $(G_k,S_k)$ such that $G_k$ is a word-hyperbolic Coxeter group, for any two generating reflections $s,t\in S_k$ the product $st$ has finite order, and the Coxeter graph…
Let $X$ be a nonempty real variety that is invariant under the action of a reflection group $G$. We conjecture that if $X$ is defined in terms of the first $k$ basic invariants of $G$ (ordered by degree), then $X$ meets a $k$-dimensional…
We study the joint distribution of descents and inverse descents over the set of permutations of n letters. Gessel conjectured that the two-variable generating function of this distribution can be expanded in a given basis with nonnegative…
The inversion number and the major index are equidistributed on the symmetric group. This is a classical result, first proved by MacMahon, then by Foata by means of a combinatorial bijection. Ever since many refinements have been derived,…
We discuss how the diffraction theory of a single translation bounded measure or a family of such measures can be understood within the framework of unitary group representations. This allows us to prove an orthogonality feature of measures…
Quantum graphs have recently been introduced as model systems to study the spectral statistics of linear wave problems with chaotic classical limits. It is proposed here to generalise this approach by considering arbitrary, directed graphs…
Let $H$ be a group, $m$ be a positive integer, $Ext_m H$ be the set of all isomorphic in $G$ classes of group monomorphisms $\varphi: H \rightarrow G$ such that index of $\varphi(H)$ in $G$ is $m$. The main goal of this paper is to describe…
We study hyperbolic polynomials with nice symmetry and express them as the determinant of a Hermitian matrix with special structure. The goal of this paper is to answer a question posed by Chien and Nakazato in 2015. By properly modifying a…
Arslan, Altoum, and Zaarour introduced an inversion statistic for generalized symmetric groups. In this work, we study the distribution of this statistic over colored permutations, including derangements and involutions. By establishing a…
In this paper, we focus on the COM-type negative binomial distribution with three parameters, which belongs to COM-type $(a,b,0)$ class distributions and family of equilibrium distributions of arbitrary birth-death process. Besides, we show…
We obtain several combinatorial results about chains, cycles and orbits of the elements of the symmetric inverse semigroup $\IS_n$ and the set $T_n$ of nilpotent elements in $\IS_n$. We also get some estimates for the growth of $|\IS_n|$…
For all integers $p>q>0$ and $k >0$, and all non-elementary torsion-free hyperbolic groups $H$, we construct a hyperbolic group $G$ in which $H$ is a subgroup, such that the distortion function of $H$ in $G$ grows like $\exp^k(n^{p/q})$.…
Bj\"orner and Wachs defined a major index for labeled plane forests and showed that it has the same distribution as the number of inversions. We define and study the distributions of a few other natural statistics on labeled forests.…