Related papers: Representation of Numerical Semigroups by Dyck Pat…
The characteristic map for the symmetric group is an isomorphism relating the representation theory of the symmetric group to symmetric functions. An analogous isomorphism is constructed for the symmetric space of symplectic forms over a…
Several recent papers have examined a rational polyhedron $P_m$ whose integer points are in bijection with the numerical semigroups (cofinite, additively closed subsets of the non-negative integers) containing $m$. A combinatorial…
Induced representations for quantum groups are defined starting from coisotropic quantum subgroups and their main properties are proved. When the coisotropic quantum subgroup has a suitably defined section such representations can be…
We consider the distribution of quadratic Gauss paths, polygonal paths joining partial sums of quadratic Gauss sums to square-free fundamental discriminant moduli in a dyadic range [Q,2Q]. We prove that this striking ensemble converges in…
We introduce and study the new combinatorial class of Dyck paths with air pockets. We exhibit a bijection with the peakless Motzkin paths which transports several pattern statistics and give bivariate generating functions for the…
This paper serves as an example to show the way we pass from semigroups to $\Gamma$-semigroups and to hypersemigroups.
In this paper, we introduce a new depicting of the so-called numerical semigroup tree $\mathcal T$. By exploring computationally this improved picture, relying on the type notion of a semigroup, we found that the number of semigroups of…
A survey of properties of the adjunction involving a semisymmetrization functor, which was suggested by J.D.H. Smith, and which maps the category of quasigroups with homotopies to the category of semisymmetric quasigroups with…
Given a graph E we define E-algebraic branching systems, show their existence and how they induce representations of the associated Leavitt path algebra. We also give sufficient conditions to guarantee faithfulness of the representations…
We investigate numerical semigroups generated by any quadratic sequence with initial term zero and an infinite number of terms. We find an efficient algorithm for calculating the Ap\'ery set, as well as bounds on the elements of the Ap\'ery…
Motivated by appearance of multisemigroups in the study of additive $2$-categories, we define and investigate the notion of a multisemigroup with multiplicities. This notion seems to be better suitable for applications in higher…
In this paper we introduce the concept of corner element of a generalized numerical semigroup, which extends in a sense the idea of conductor of a numerical semigroup to generalized numerical semigroups in higher dimensions. We present…
In this paper, we systematically study generalized Markov numbers arising from semigroups of reduced integer matrices. This construction allows us to find these numbers by counting perfect matchings of a new family of bipartite graphs,…
In this work we explore the structure of the branching graph of the unitary group using Schur transitions. We find that these transitions suggest a new combinatorial expression for counting paths in the branching graph. This formula, which…
A path integral representation is given for the solutions of the 3+1 dimensional Dirac equation. The regularity of the trajectories, the non-relativistic limit and the semiclassical approximation are briefly mentioned.
The recent proof of the Boij-Soederberg conjectures reveals new structure about Betti diagrams of modules, giving a complete description of the cone of Betti diagrams. We begin to expand on this new structure by investigating the semigroup…
This paper gives an introduction to the homotopy theory of quasi-categories. Weak equivalences between quasi-categories are characterized as maps which induce equivalences on a naturally defined system of groupoids. These groupoids…
In this paper we study the practicality and usefulness of incorporating distributed representations of graphs into models within the context of drug pair scoring. We argue that the real world growth and update cycles of drug pair scoring…
The pseudoparticle approach is a numerical method to compute path integrals without discretizing spacetime. The basic idea is to consider only those field configurations, which can be represented as a linear superposition of a small number…
A class of subgroups is obtained for symmetric groups using signed Brauer diagrams.