Related papers: On partitions associated with elementary symmetric…
Quickly convergent series are given to compute polyzeta numbers. The formula involves an intricate combination of (generalized) polylogarithms at 1/2. However, the combinatorics has a very simple geometric interpretation: it corresponds…
Classical mathematics are founded within set theory, but sets don't have \emph{symmetries}. We conjecture that if we allow sets with symmetries, then many problems such as \emph{Mirror symmetry} or \emph{Homological mirror symmetry} can be…
We study the symmetry properties of autonomous integrating factors from an algebraic point of view. The symmetries are delineated for the resulting integrals treated as equations and symmetries of the integrals treated as functions or…
We introduce the notion of "quasi-symmetric" polynomials, which is a generalization of the notion of symmetry, and is particularly suited to the setting of polynomial rings over finite fields. The properties of this new class of functions…
In this paper, we propose a useful replacement for quicksort-style utility functions. The replacement is called Symmetry Partition Sort, which has essentially the same principle as Proportion Extend Sort. The maximal difference between them…
We review some connections between quantum information and statistical mechanics. We focus on three sets of results for classical spin models. First, we show that the partition function of all classical spin models (including models in…
Simplicial partitions are a fundamental structure in computational geometry, as they form the basis of optimal data structures for range searching and several related problems. Current algorithms are built on very specific spatial…
Solution and analysis of mathematical programming problems may be simplified when these problems are symmetric under appropriate linear transformations. In particular, a knowledge of the symmetries may help reduce the problem dimension, cut…
We present the basic elements of a generalization of symmetric function theory involving functions of commuting and anticommuting (Grassmannian) variables. These new functions, called symmetric functions in superspace, are invariant under…
We consider the value distribution of logarithms of symmetric power L-functions associated with newforms of even weight and prime power level. In the symmetric square case, under certain plausible analytical conditions, we prove that…
We define a generalized vector partition function and derive an identity for generating series of such functions associated with solutions of basic recurrence relation of combinatorial analysis. As a consequence, we obtain the generating…
This article is devoted to the study of several algebras which are related to symmetric functions, and which admit linear bases labelled by various combinatorial objects: permutations (free quasi-symmetric functions), standard Young…
We give an explicit expression of the normalized characters of the symmetric group in terms of the contents of the partition labelling the representation.
We describe all proper holomorphic mappings of the symmetrized polydisc and study its geometric properties. We also apply the obtained results to the study of the spectral unit ball in $\MM_n(\CC^n)$.
The Verschiebung operators $\varphi_t $ are a family of endomorphisms on the ring of symmetric functions, one for each integer $t\geq2$. Their action on the Schur basis has its origins in work of Littlewood and Richardson, and is intimately…
The exactly solvable four-vertex model with the fixed boundary conditions in the presence of inhomogeneous linearly growing external field is considered. The partition function of the model is calculated and represented in the determinantal…
We examine two associative products over the ring of symmetric functions related to the intransitive and Cartesian products of permutation groups. As an application, we give an enumeration of some Feynman type diagrams arising in Bender's…
It is known that a graph isomorphism testing algorithm is polynomially equivalent to a detecting of a graph non-trivial automorphism algorithm. The polynomiality of the latter algorithm, is obtained by consideration of symmetry properties…
It is well-known that the convex and concave envelope of a multilinear polynomial over a box are polyhedral functions. Exponential-sized extended and projected formulations for these envelopes are also known. We consider the convexification…
The injective polynomial modules for a general linear group $G$ of degree $n$ are labelled by the partitions with at most $n$ parts. Working over an algebraically closed field of characteristic $p$, we consider the question of which…