Related papers: Random permutations from $q$-Demazure products
Permutons are probability measures on the unit square with uniform marginals that provide a natural way to describe limits of permutations. We are interested in the permuton limits for permutations sampled uniformly from certain…
We present the convergence rates of synchronous and asynchronous Q-learning for average-reward Markov decision processes, where the absence of contraction poses a fundamental challenge. Existing non-asymptotic results overcome this…
The probability that a random permutation in $S_n$ is a derangement is well known to be $\displaystyle\sum\limits_{j=0}^n (-1)^j \frac{1}{j!}$. In this paper, we consider the conditional probability that the $(k+1)^{st}$ point is fixed,…
Let $A(1):=k[X]/(X^p)$ be the natural representation of the Witt algebra $W(1)$ over an algebraically closed field of prime characteristic $p>3$. In this note, we decompose the $W(1)$-module $A(1)\otimes A(1)$ into two invariant subspaces,…
Rudolph conjectures that for permutations $p$ and $q$ of the same length, $A_n(p) \le A_n(q)$ for all $n$ if and only if the spine structure of $T(p)$ is less than or equal to the spine structure of $T(q)$ in refinement order. We prove one…
The complexity of maximal likelihood decoding of the Reed-Solomon codes $[q-1, k]_q$ is a well known open problem. The only known result in this direction states that it is at least as hard as the discrete logarithm in some cases where the…
In recent years there has been significant progress in the study of products of subsets of finite groups and of finite simple groups in particular. In this paper we consider which families of finite simple groups $G$ have the property that…
The relativistic finite-difference SUSY Quantum Mechanics (QM) is developed. We show that it is connected in a natural way with the q-deformed SUSY Quantum Mechanics. Simple examples are given.
The conflation of a finite number of probability distributions P_1,..., P_n is a consolidation of those distributions into a single probability distribution Q=Q(P_1,..., P_n), where intuitively Q is the conditional distribution of…
We review the W_N algebra and its quantum deformation, based on free field realizations. The (quantum deformed) W_N algebra is defined through the (quantum deformed) Miura transformation, and its singular vectors realize the Jack…
The investigation of the q deformation of the S-matrix for excitations on the string world sheet in AdS5 x S5 is continued. We argue that due to the lack of Lorentz invariance the situation is more subtle than in a relativistic theory in…
We present an approach to classical definitions and results on cumulant--moment relations and Wick polynomials based on extensive use of convolution products of linear functionals on a coalgebra. This allows, in particular, to understand…
Consider a random permutation of $\{1, \ldots, \lfloor n^{t_2}\rfloor\}$ drawn according to the Ewens measure with parameter $t_1$ and let $K(n, t)$ denote the number of its cycles, where $t\equiv (t_1, t_2)\in\mathbb [0, 1]^2$. Next,…
The $q$-multinomial coefficient, a classical object in enumerative combinatorics, counts permutations of multisets weighted by the number of inversions, with a single deformation parameter $q$. We introduce the twisted multinomial…
We compute the expected number of commutations appearing in a reduced word for the longest element in the symmetric group. The asymptotic behavior of this value is analyzed and shown to approach the length of the permutation, meaning that…
We consider a natural $q$-deformation of the classical Markov numbers. This $q$-deformation is closely related to $q$-deformed rational numbers recently introduced by two of us. Both notions, those of $q$-rationals and $q$-Markov numbers,…
We study scaling limits of random permutations ("permutons") constrained by having fixed densities of a finite number of patterns. We show that the limit shapes are determined by maximizing entropy over permutons with those constraints. In…
In the usual approach to q-deformed gauge theories, the gauge fields are required to be non-local or non-commutative one's. If we introduce, however, an extended product, which we call `` $\star$-product\rq\rq, among the generators of a…
We first observe a mysterious similarity between the braid arrangement and the arrangement of all hyperplanes in a vector space over the finite field $\mathbb{F}_q$. These two arrangements are defined by the determinants of the Vandermonde…
We present decidability results for termination of classes of term rewriting systems modulo permutative theories. Termination and innermost termination modulo permutative theories are shown to be decidable for term rewrite systems (TRS)…