Related papers: One-parameter groups and combinatorial physics
The probability that the commutator of two group elements is equal to a given element has been introduced in literature few years ago. Several authors have investigated this notion with methods of the representation theory and with…
In this paper we define generalizations of boson normal ordering. These are based on the number of contractions whose vertices are next to each other in the linear representation of the boson operator function. Our main motivation is to…
We classify one-element extensions of a hyperplane arrangement by the induced adjoint arrangement. Based on the classification, several kinds of combinatorial invariants including Whitney polynomials, characteristic polynomials, Whitney…
This is a survey of recent progress in several areas of combinatorial algebra. We consider combinatorial problems about free groups, polynomial algebras, free associative and Lie algebras. Our main idea is to study automorphisms and, more…
In this article combinatorial aspects of normal ordering annihilation and creation operators of a multi-mode boson system are discussed. The modes are assumed to be coupled since otherwise the problem of normal ordering is reduced to the…
We consider the problem of characterizing the class of those permutation groups that are the symmetry groups of Boolean functions. These are exactly the automorphism groups of hypergraphs. They are also called the relation groups. In this…
We discuss two distinct aspects in supersymmetric quantum mechanics. First, we introduce a new class of operators A and $\bar{A}$ in terms of anticommutators between the momentum operator and N+1 arbitrary superpotentials. We show that…
We give a review of modern approaches to constructing formal solutions to integrable hierarchies of mathematical physics, whose coefficients are answers to various enumerative problems. The relationship between these approaches and…
This work focuses on the combinatorial properties of glued semigroups and provides its combinatorial characterization. Some classical results for affine glued semigroups are generalized and some methods to obtain glued semigroups are…
We introduce the theoretical framework we use to study the bewildering variety of phases in condensed--matter physics. We emphasize the importance of the breaking of symmetries, and develop the idea of an order parameter through several…
We express the Partial regularities and $a^*$-invariants of a Borel type ideal in terms of its irredundant irreducible decomposition. In addition we consider the behaviours of those invariants under intersections and sums.
Composite structure of particles somewhat modifies their statistics, compared to the pure Bose- or Fermi-ones. The spin-statistics theorem, so, is not valid anymore. Say, $\pi$-mesons, excitons, Cooper pairs are not ideal bosons, and,…
We analyze the structure of one-parameter subgroups of SO(3,2). We find two new types of subgroups in comparison with the structure of the one-parameter subgroups of SO(2,2), and we construct explicit examples for these subgroups. We also…
It is proved that the numerical semigroups associated to the combinatorial configurations satisfy a family of non-linear symmetric patterns. Also, these numerical semigroups are studied for two particular classes of combinatorial…
Many random combinatorial objects have a component structure whose joint distribution is equal to that of a process of mutually independent random variables, conditioned on the value of a weighted sum of the variables. It is interesting to…
Modeling potential alloys requires the exploration of all possible configurations of atoms. Additionally, modeling the thermal properties of materials requires knowledge of the possible ways of displacing the atoms. One solution to finding…
The general form of the operators commuting with the ground representation (appearing in many physical problems within single particle approximation) of the group is found. With help of the modified group projector technique, this result is…
Wigner's particle classification provides for "continuous spin" representations of the Poincar\'e group, corresponding to a class of (as yet unobserved) massless particles. Rather than building their induced realizations by use of "Wigner…
The composite character of two-fermion bosons manifests itself in the interference of many composites as a deviation from the ideal bosonic behavior. A state of many composite bosons can be represented as a superposition of different…
Let $G$ be a finite abelian group and $A$ a subset of $G$. The spectrum of $A$ is the set of its large Fourier coefficients. Known combinatorial results on the structure of spectrum, such as Chang's theorem, become trivial in the regime…