Related papers: Estimating Certain Non-Zero Littlewood-Richardson …
NOTE: PAPER WITHDRAWN (See Comments) The Clifford and Local Clifford groups for $d > 2$ dimensional systems have been topics of recent interest due to their applications in graph states, quantum codes, and possible applications in fast…
Widely applicable, modified Green-Kubo expressions for the local diffusion coefficient ($D_l$) are obtained using linear response theory. In contrast to past definitions in use, these expressions are statistical mechanical results.…
In this paper, developing a new approach based on Fourier analysis methods for dispersive PDEs, we establish a low regularity NLS approximation for the one-dimensional cubic Klein-Gordon equation. Our main result includes energy class…
In this short note we have proved an enhanced version of a theorem of Lorentz [1] and its generalization to the multivariate case which gives a non- uniform estimate of degree of approximation by a polynomial with positive coefficients. The…
Given a basis for a polynomial ring, the coefficients in the expansion of a product of some of its elements in terms of this basis are called linearization coefficients. These coefficients have combinatorial significance for many classical…
We produce a family of reductions for Schubert intersection problems whose applicability is checked by calculating a linear combination of the dimensions involved. These reductions do not alter the Littlewood-Richardson coefficient, and…
This is a companion paper to arXiv:0909.2280. It is mostly expository and focuses on the representation-theoretic and combinatorial aspects of the main problems considered in the other article.
The purpose of this text is twofold. We present a review of the existing stability results for Sobolev, Hardy-Littlewood-Sobolev (HLS) and related inequalities. We also contribute to the topic with some observations on constructive…
We present an extension of the famous Littlewood-Offord problem when Bernoulli distributions are replaced with discrete log-concave distributions. A variant of the Littlewood-Offord problem for arithmetic progressions, as well as an…
We give a survey of the representation theory of $\mathrm{GL}_N$ over finite local principal ideal rings via Clifford theory, with an emphasis on the construction of regular representations. We review results of Shintani and Hill, and the…
An alternative representation of an exact statistical field theory for simple fluids, based on the method of collective variables, is presented. The results obtained are examined from the point of another version of theory that was…
A "Littlewood polynomial" is a polynomial whose coefficients are all 1 or -1. The set of all complex roots of all Littlewood polynomials exhibits many complicated, beautiful and fascinating patterns. Some fractal regions of this set closely…
We use character polynomials to obtain a positive combinatorial interpretation of the multiplicity of the sign representation in irreducible polynomial representations of $GL_n(\mathbb{C})$ indexed by two-column and hook partitions. Our…
Littlewood-Richardson rule gives the decomposition formula for the multiplication of two Schur functions, while the decomposition formula for the multiplication of two Hall-Littlewood functions or two universal characters is also given by…
The stretched Littlewood-Richardson coefficient $c^{t\nu}_{t\lambda,t\mu}$ was conjectured by King, Tollu, and Toumazet to be a polynomial function in $t.$ It was shown to be true by Derksen and Weyman using semi-invariants of quivers.…
This paper deals with Poisson approximation to weighted sums of locally dependent random variables using Stein's method. The derived result represents a significant improvement of existing results. To illustrate the effectiveness of our…
There is given a characterization of the geometric distribution by the independence of linear forms with random coefficients. The result is a discrete analog of the corresponding theorem on exponential distribution. The property of linear…
We find and prove a factorization formula for certain Macdonald Littlewood-Richardson coefficients $c_{\lambda\mu}^{\nu}(q,t)$. Namely, we consider the case that the Kostka number $K_{\mu, \nu -\lambda}$ is $1$. This settles a particular…
Statistical and probabilistic characteristics of locally free group with growing number of generators are defined and their application to statistics of braid groups is given.
For a given skew shape, we build a crystal graph on the set of all reverse plane partitions that have this shape. As a consequence, we get a simple extension of the Littlewood-Richardson rule for the expansion of the corresponding dual…