Related papers: On Descents in Standard Young Tableaux

We suggest an approach for the enumeration of minimal permutations having d descents which uses skew Young tableaux. We succeed in finding a general expression for the number of such permutations in terms of (several) sums of determinants.…

The notion of a barely set-valued semistandard Young tableau was introduced by Reiner, Tenner and Yong in their study of the probability distribution of edges in the Young lattice of partitions. Given a partition $\lambda$ and a positive…

The deviations from a purely exponential behavior in a decay process are analyzed in relation to Van Hove's "\lambda^2 t" limiting procedure. Our attention is focused on the effects that arise when the coupling constant is small but…

A cyclic descent function on standard Young tableaux of size $n$ is a function that restricts to the usual descent function when $n$ is omitted, such that the number of standard Young tableaux of given shape with cyclic descent set…

This paper gives upper and lower bounds on the gap in Jensen's inequality, i.e., the difference between the expected value of a function of a random variable and the value of the function at the expected value of the random variable. The…

We study the inductive biases of diffusion models with a conditioning-variable, which have seen widespread application as both text-conditioned generative image models and observation-conditioned continuous control policies. We observe that…

We consider two questions of Wilf related to Standard Young Tableaux. We provide a partial answer to one question, and that will lead us to a more general answer to the other question. Our answers are purely combinatorial.

In this note, we consider a fixed vector field $V$ on $S^2$ and study the distribution of points which lie on the nodal set (of a random spherical harmonic) where $V$ is also tangent. We show that the expected value of the corresponding…

As a natural generalization of permutations, transversals of Young diagrams play an important role in the study of pattern avoiding permutations. Let $\mathcal{T}_{\lambda}(\tau)$ and $\mathcal{ST}_{\lambda}(\tau)$ denote the set of…

Given two vectors $u$ and $v$, their outer sum is given by the matrix $A$ with entries $A_{ij} = u_{i} + v_{j}$. If the entries of $u$ and $v$ are increasing and sufficiently generic, the total ordering of the entries of the matrix is a…

The number of Young Tableaux whose shape is a k by n rectangle is famously (nk)! 0! ... (k-1)!/((n+k-1)!(n+k-2)!... n!) implying that for each specific k, that sequence satisfies a linear recurrence equation with polynomial coefficients of…

In this paper we derive sharp lower and upper bounds for the covariance of two bounded random variables when knowledge about their expected values, variances or both is available. When only the expected values are known, our result can be…

The study of representations of affine Hecke algebras has led to a new notion of shapes and standard Young tableaux which works for the root system of any finite Coxeter group. This paper is completely independent of affine Hecke algebra…

The Evans function is an analytic function that encodes information about the intersection of certain subspaces in ODE boundary value problems. As such it is a useful tool for computing the spectrum of boundary value problems arising in the…

Given a random word of size $n$ whose letters are drawn independently from an ordered alphabet of size $m$, the fluctuations of the shape of the random RSK Young tableaux are investigated, when $n$ and $m$ converge together to infinity. If…

Young tableaux are ubiquitous in various branches of mathematics. There are two counting formulas for standard Young tableaux. The first involves a determinant and goes back to Frobenius and Young, and the second is the hook formula by…

Standard set-valued Young tableaux are a generalization of standard Young tableaux where cells can contain unordered sets of integers, with the added condition that every integer at position $(i,j)$ must be smaller that every integer at…

The main purpose of this paper is to establish a noncommutative analogue of the Efron--Stein inequality, which bounds the variance of a general function of some independent random variables. Moreover, we state an operator version including…

We present a bijection between the set of standard Young tableaux of staircase minus rectangle shape, and the set of marked shifted standard Young tableaux of a certain shifted shape. Numerically, this result is due to DeWitt (2012).…

We introduce the notion of "type" of a tableau, that allows us to define new families of tableaux including both balanced and standard Young tableaux. We use these new objects to describe the set of reduced decompositions of any…