Related papers: System of recursive equations for the partition fu…
We consider consistent particle systems, which include independent random walkers, the symmetric exclusion and inclusion processes, as well as the dual of the KMP model. Consistent systems are such that the distribution obtained by first…
A method for calculating the $1/d$ expansion coefficients for solutions of integration by parts relations for Feynman integrals is presented. The idea is to use linear substitutions to transform these relations to an explicitly recursive…
The general scheme for the treatment of relaxation processes and temporal autocorrelations of dynamical variables for many particle systems is presented in framework of the recurrence relations approach. The time autocorrelation functions…
In this work we express the partition function of the integrable elliptic solid-on-solid model with domain-wall boundary conditions as a single determinant. This representation appears naturally as the solution of a system of functional…
We present a finite-order system of recurrence relations for a permanent of circulant matrices containing a band of k any-value diagonals on top of a uniform matrix (for k = 1, 2, and 3) as well as the method for deriving such recurrence…
We discuss first order systems of rational difference equations which have the property that lines through the origin are mapped into lines through the origin. We call such systems projective systems of rational difference equations and we…
We revisit games in partition function form, i.e. cooperative games where the payoff of a coalition depends on the partition of the entire set of players. We assume that each coalition computes its worth having probabilistic beliefs over…
In this paper we introduce a family of rational approximations of the reciprocal of a $\phi$-function involved in the explicit solutions of certain linear differential equations, as well as in integration schemes evolving on manifolds. The…
Let $A\subset \N_{+}$ and by $P_{A}(n)$ denotes the number of partitions of an integer $n$ into parts from the set $A$. The aim of this paper is to prove several result concerning the existence of integer solutions of Diophantine equations…
In this paper, we study various classes of partition functions such as those related to the parity of the number of parts, to differences of partition numbers, and to partitions with a repeated smallest part. We establish identities…
We consider the six-vertex model on an $N \times N$ square lattice with the domain wall boundary conditions. Boundary one-point correlation functions of the model are expressed as determinants of $N\times N$ matrices, generalizing the known…
The recursion relations are derived for multi-photon processes of noncommutative QED. The relations concern purely photonic processes as well as the processes with two fermions involved, both for arbitrary number of photons at tree level.…
Functional equations satisfied by additive functions have a special interest not only in the theory of functional equations, but also in the theory of (commutative) algebra because the fundamental notions such as derivations and…
We investigate certain classes of integrable classical or quantum spin systems. The first class is characterized by the recursively defined property $P$ saying that the spin system consists of a single spin or can be decomposed into two…
The inverse problem method is tested for a class of mean field statistical mechanics models representing a mixture of particles of different species. The robustness of the inversion is investigated for different values of the physical…
We present a detailed analysis of the spin models with near-neighbors interactions constructed in our previous paper [Phys. Lett. B 605 (2005) 214] by a suitable generalization of the exchange operator formalism. We provide a complete…
This letter is concerned with the analysis of the six-vertex model with domain-wall boundaries in terms of partial differential equations (PDEs). The model's partition function is shown to obey a system of PDEs resembling the celebrated…
We consider estimation procedures which are recursive in the sense that each successive estimator is obtained from the previous one by a simple adjustment. We study rate of convergence of recursive estimation procedures for the general…
Motivated by the study of systems of higher order boundary value problems with functional boundary conditions, we discuss, by topological methods, the solvability of a fairly general class of systems of perturbed Hammerstein integral…
In this article we will derive a combinatorial formula for the partition function p(n). In the second part of the paper we will establish connection between partitions and q-binomial coefficients and give new interpretation for q-binomial…