Related papers: Partition Functions and Kurepa Decomposition I: Al…

This article gives a natural decomposition of the suspension of generalized moment-angle complexes or {\it partial product spaces} which arise as {\it polyhedral product functors} described below. In the special case of the complements of…

We investigate the properties of the moments of the cot function using the central factorial numbers. Using a new integral representation of the central factorial numbers, we find a new way to express these moments in terms of recursive…

The quantum version of Olbert's kappa distribution applicable to fermions is obtained. Its construction is straightforward but requires recognition of the differences in the nature of states separated by Fermi momenta. Its complement, the…

The partition functions $P(n,m,p)$, the number of integer partitions of $n$ into exactly $m$ parts with each part at most $p$, and $Q(n,m,p)$, the number of integer partitons of $n$ into exactly $m$ distinct parts with each part at most…

A full characterization of $(p,q)$-deformed Fibonacci and Lucas polynomials is given. These polynomials obey non-conventional three-term recursion relations. Their generating functions and Fourier integral transforms are explicitly computed…

In this paper we consider the functional equation for alternating factorial sum and some of its particular solutions (alternating Kurepa's function $A(z)$ from [Petojevic_02] and function $A_{1}(z)$). We determine an extension of domain of…

I review the basic idea of $k_{\perp}$-factorization and its relation to collinear factorization. Theoretical results in resummed perturbation theory are summarized and the example of the heavy-flavour structure functions is explicitly…

Decompositional theories describe the ways in which a global physical system can be split into subsystems, facilitating the study of how different possible partitions of a same system interplay, e.g. in terms of inclusions or signalling. In…

The present paper is a continuation of our work [11], where we introduced a fractional operator calculus related to a fractional ${\psi}-$Fueter operator in the one-dimensional Riemann-Liouville derivative sense in each direction of the…

Using an explicit computable expression of ordinary multinomials, we establish three remarkable connections, with the q-generalized Fibonacci sequence, the exponential partial Bell partition polynomials and the density of convolution powers…

We consider kernels of discrete convolution operators or, equivalently, homogeneous solutions of partial difference operators and show that these solutions always have to be exponential polynomials. The respective polynomial space in…

Although symmetry methods and analysis are a necessary ingredient in every physicist's toolkit, rather less use has been made of combinatorial methods. One exception is in the realm of Statistical Physics, where the calculation of the…

We introduce a collection of polynomials $F_N$, associated to each positive integer $N$, whose divisibility properties yield a reformulation of the Goldbach conjecture. While this reformulation certainly does not lead to a resolution of the…

In this contribution we announce a complete classification and new exotic phenomena of the meromorphic structure of $\z$-functions associated to conic manifolds proved in \cite{KLP1}. In particular, we show that the meromorphic extensions…

It is classical that univariate algebraic functions satisfy linear differential equations with polynomial coefficients. Linear recurrences follow for the coefficients of their power series expansions. We show that the linear differential…

For linear operators which factor with suitable assumptions concerning commutativity of the factors, we introduce several notions of a decomposition. When any of these hold then questions of null space and range are subordinated to the same…

Starting from Ritt's classical theorems, we give a survey of results in functional decomposition of polynomials and of applications in Diophantine equations. This includes sufficient conditions for the indecomposability of polynomials, the…

In this thesis quadratic and cubic algebras, which are extensions of SU(1,1) and SU(2) are studied in detail, with particular attention being given to their construction, their finite and infinite dimensional irreducible representations and…

In this article, we define and study a geometry and an order on the set of partitions of an even number of objects. One of the definitions involves the partition algebra, a structure of algebra on the set of such partitions depending on an…

Set partitions and permutations with restrictions on the size of the blocks and cycles are important combinatorial sequences. Counting these objects lead to the sequences generalizing the classical Stirling and Bell numbers. The main focus…