相关论文: Descent Functions and Random Young Tableaux
Functional equations (FE) arise quite naturally in the analysis of stochastic systems of different kinds : queueing and telecommunication networks, random walks, enumeration of planar lattice walks, etc. Frequently, the object is to…
We investigate in some detail a recently suggested general class of ensembles of sparse undirected random graphs based on a hidden stub-coloring, with or without the restriction to nondegenerate graphs. The calculability of local and global…
The Collatz variations pattern seems not to have any recurrence relation between numbers. But knowing that there is at least a natural number that converges after several iterations we construct a function $f_{X,Y}$ that is equal to the…
Using lattice path counting arguments, we reproduce a well known formula for the number of standard Young tableaux. We also produce an interesting new formula for tableaux of height $\leq 3$ using the Fourier methods of Ault and Kicey.
The law of large numbers extends to random sets by employing Minkowski addition. Above that, a central limit theorem is available for set-valued random variables. The existing results use abstract isometries to describe convergence of the…
We give new bounds and asymptotic estimates on the number of standard Young tableaux of skew shape in a variety of special cases. Our approach is based on Naruse's hook-length formula. We also compare our bounds with the existing bounds on…
The stochastic gradient descent has been widely used for solving composite optimization problems in big data analyses. Many algorithms and convergence properties have been developed. The composite functions were convex primarily and…
The number of standard Young tableaux of a fixed shape is famously given by the hook-length formula due to Frame, Robinson and Thrall. A bijective proof of Novelli, Pak and Stoyanovskii relies on a sorting algorithm akin to jeu-de-taquin…
In this work we are considering the behavior of the limit shape of Young diagrams associated to random permutations on the set $\{1,\dots,n\}$ under a particular class of multiplicative measures. Our method is based on generating functions…
The main goal of this paper is to obtain sufficient conditions so that Le Roy type functions and multivariate Le Roy type functions satisfy subordination of exponential function. Moreover conditions on parameters have been derived to claim…
In special relativity the mathematical expressions, defining physical observables as the momentum, the energy etc, emerge as one parameter (light speed) continuous deformations of the corresponding ones of the classical physics. Here, we…
We enumerate derangements with descents in prescribed positions. A generating function was given by Guo-Niu Han and Guoce Xin in 2007. We give a combinatorial proof of this result, and derive several explicit formulas. To this end, we…
The work performed on a system in a microcanonical state by changes in a control parameter is characterized in terms of its statistics. The transition probabilities between eigenstates of the system Hamiltonians at the beginning and the end…
Walks on Young's lattice of integer partitions encode many objects of algebraic and combinatorial interest. Chen et al. established connections between such walks and arc diagrams. We show that walks that start at $\varnothing$, end at a…
We consider the distribution of the major index on standard tableaux of arbitrary straight shape and certain skew shapes. We use cumulants to classify all possible limit laws for any sequence of such shapes in terms of a simple auxiliary…
Motivated by the properties of the descent polynomials, which enumerate permutations of $S_n$ with a fixed descent set, we define descent polynomials for labeled rooted trees. We give recursive and explicit formulas for these polynomials…
An increasing tableau is a semistandard tableau with strictly increasing rows and columns. It is well known that the Catalan numbers enumerate both rectangular standard Young tableaux of two rows and also Dyck paths. We generalize this to a…
Observed clusters should be modelled by considering the distribution function to be a random variable that quantifies the degree of excitation of the system's normal modes. A system of canonical coordinates for the space of DFs is…
This article describes a sequence of rational functions which converges locally uniformly to the zeta function. The numerators (and denominators) of these rational functions can be expressed as characteristic polynomials of matrices that…
We define a counting function that is related to the binomial coefficients. An explicit formula for this function is proved. In some particular cases, simpler explicit formuls are derived. We also derive a formula for the number of…