Related papers: Data-scientific study of Kronecker coefficients

Let $p_n$ be the number of partitions of an integer $n$. For each of the partition statistics of counting their parts, ranks, or cranks, there is a natural family of integer polynomials. We investigate their asymptotics and the limiting…

What might a combinatorial interpretation of the Kronecker coefficients even look like? We introduce a class of combinatorial objects called bitableaux, which we believe are a natural candidate, and we formulate a purely combinatorial…

We consider functional data which have only been observed on a subset of their domain. This paper aims to develop statistical tests to determine whether the function and the domain over which it is observed are independent. The assumption…

We propose a new approach to study plethysm coefficients by using the Schur-Weyl duality between the symmetric group and the partition algebra. This allows us to explain the stability properties of plethysm and Kronecker coefficients in a…

We examine the convergence properties of sequences of nonnegative real numbers that satisfy a particular class of recursive inequalities, from the perspective of proof theory and computability theory. We first establish a number of results…

A partition polynomial is a refinement of the partition number p(n) whose coefficients count some special partition statistic. Just as partition numbers have useful asymptotics so do partition polynomials. In fact, their asymptotics…

It is known that the Kronecker coefficient of three partitions is a bounded and weakly increasing sequence if one increases the first part of all three partitions. Furthermore if the first parts of partitions \lambda,\mu are big enough then…

These lecture notes introduce quantum spin systems and several computational methods for studying their ground-state and finite-temperature properties. Symmetry-breaking and critical phenomena are first discussed in the simpler setting of…

We give an example in which it is possible to understand quantum statistics using classical concepts. This is done by studying the interaction of charged matter oscillators with the thermal and zeropoint electromagnetic fields…

In this paper we give a new sufficient condition for a general stability of Kronecker coefficients, which we call it additive stability. It was motivated by a recent talk of J. Stembridge at the conference in honor of Richard P. Stanley's…

Conditional independence is a fundamental concept in many areas of statistical research, including, for example, sufficient dimension reduction, causal inference, and statistical graphical models. In many modern applications, data arise in…

In real world applications dealing with compositional datasets, it is easy to face the presence of structural zeros. The latter arise when, due to physical limitations, one or more variables are intrinsically zero for a subset of the…

We define the coherence non-activating measurement as the positive operator-valued measurement which gives the same result whether or not the coherence in a quantum state is destroyed. A connection is built between the coherence activating…

This is a survey on the use of low-degree polynomials to predict and explain the apparent statistical-computational tradeoffs in a variety of average-case computational problems. In a nutshell, this framework measures the complexity of a…

Compositional data (i.e., data comprising random variables that sum up to a constant) arises in many applications including microbiome studies, chemical ecology, political science, and experimental designs. Yet when compositional data serve…

Although G\"odel's incompleteness theorem made mathematician recognize that no axiomatic system could completely prove its correctness and that there is an eternal hole between our knowledge and the world, physicists so far continue to work…

In this paper we propose and study a class of simple, nonparametric, yet interpretable measures of conditional dependence between two random variables $Y$ and $Z$ given a third variable $X$, all taking values in general topological spaces.…

This paper consists of two prongs. Firstly, we prove that any Specht module labelled by a 2-separated partition is semisimple and we completely determine its decomposition as a direct sum of graded simple modules. Secondly, we apply these…

We introduce a rigorous framework for the quantification of coherence and identify intuitive and easily computable measures of coherence. We achieve this by adopting the viewpoint of coherence as a physical resource. By determining defining…

This paper considers the problem of testing whether there exists a solution satisfying certain non-negativity constraints to a linear system of equations. Importantly and in contrast to some prior work, we allow all parameters in the system…