Related papers: Young Diagram Decompositions for Almost Symmetric …
This work extends the results known for the Delta sets of non-symmetric numerical semigroups with embedding dimension three to the symmetric case. Thus, we have a fast algorithm to compute the Delta set of any embedding dimension three…
We derive new combinatorial identities which may be viewed as multivariate analogs of summation formulas for hypergeometric series. As in the previous paper [Re], we start with probability distributions on the space of the infinite Young…
With modern computers we can compute nuclear many-body wave functions with an astounding number of component, $ > 10^{10}$. But, aside from reproducing and/or predicting experiments, what do we learn from vectors with tens of billions of…
A \emph{numerical semigroup} is a subset $\Lambda$ of the nonnegative integers that is closed under addition, contains $0$, and omits only finitely many nonnegative integers (called the \emph{gaps} of $\Lambda$). The collection of all…
We present a semi-parametric approach to photographic image synthesis from semantic layouts. The approach combines the complementary strengths of parametric and nonparametric techniques. The nonparametric component is a memory bank of image…
Totally symmetric sets are a recently introduced tool for studying homomorphisms between groups. In this paper, we give full classifications of totally symmetric sets in certain families of groups and bound their sizes in others. As a…
Networks play a prominent role in the study of complex systems of interacting entities in biology, sociology, and economics. Despite this diversity, we demonstrate here that a statistical model decomposing networks into matching and…
This paper studies planar algebras of Jones' style associated with the Young graph. We first see that, given a positive real valued function on the Young graph, we may obtain a planar algebra whose structure is defined in terms of a state…
A numerical semigroup is a subset of N containing 0, closed under addition and with finite complement in N. An important example of numerical semigroup is given by the Weierstrass semigroup at one point of a curve. In the theory of…
A quasi-automatic semigroup is defined by a finite set of generators, a rational (regular) set of representatives, such that if a is a generator or neutral, then the graph of right multiplication by a on the set of representatives is a…
This paper has several purposes. We present through a critical review the results from already published papers on the constructive semigroup theory, and contribute to its further development by giving solutions to open problems. We also…
In this paper we present a new kind of semigroups called convex body semigroups which are generated by convex bodies of R^k. They generalize to arbitrary dimension the concept of proportionally modular numerical semigroup of [7]. Several…
In this paper, we consider a question of sum-keeping about a multiplicative subsemigroup and its generator subsets in a semiring, and develop some elementary (collapse) process of the sum-keeping retraction through subsets until one minimal…
Given two structures $\mathcal{M}$ and $\mathcal{N}$ on the same domain, we say that $\mathcal{N}$ is a reduct of $\mathcal{M}$ if all $\emptyset$-definable relations of $\mathcal{N}$ are $\emptyset$-definable in $\mathcal{M}$. In this…
Symmetries impose structure on the Hilbert space of a quantum mechanical model. The mathematical units of this structure are the irreducible representations of symmetry groups and I consider how they function as conceptual units of…
In this paper we introduce the notion of extension of a numerical semigroup. We provide a characterization of the numerical semigroups whose extensions are all arithmetic and we give an algorithm for the computation of the whole set of…
The fusion procedure provides a way to construct new solutions to the Yang-Baxter equation. In the case of the symmetric group the fusion procedure has been used to construct diagonal matrix elements using a decomposition of the Young…
We investigate subsets of the symmetric group with structure similar to that of a graph. The trees of these subsets correspond to minimal conjugate generating sets of the symmetric group. There are two main theorems in this paper. The first…
In this paper we introduce a new homology theory devoted to the study of families such as semi-algebraic or subanalytic families and in general to any family definable in an o-minimal structure (such as Denjoy-Carleman definable or $ln-exp$…
AGT relations imply that the four-point conformal block admits a decomposition into a sum over pairs of Young diagrams of essentially rational Nekrasov functions - this is immediately seen when conformal block is represented in the form of…