相关论文: Enumerating meandric systems with large number of …

We consider the concept of irreducible meandric system introduced by Lando and Zvonkin. We place this concept in the lattice framework of NC(n). As a consequence, we show that the even generating function for irreducible meandric systems is…

We study compositions of a positive integer $n$ in which the occurrence of even parts larger than a fixed threshold $k$ is controlled. More precisely, for each composition $m=(m_1,\dots,m_r)$ we consider the number of even parts strictly…

We study discrete probabilistic programs with potentially unbounded looping behaviors over an infinite state space. We present, to the best of our knowledge, the first decidability result for the problem of determining whether such a…

We examine two different ways of encoding a counting function, as a rational generating function and explicitly as a function (defined piecewise using the greatest integer function). We prove that, if the degree and number of input…

We study generating functions in the context of Rota-Baxter algebras. We show that exponential generating functions can be naturally viewed in a very special case of complete free commutative Rota-Baxter algebras. This allows us to use free…

We count the number of irreducible polynomials in several variables of a given degree over a finite field. The results are expressed in terms of a generating series, an exact formula and an asymptotic approximation. We also consider the…

The recently developed theory of extended generating functions of symplectic maps are combined with methods to prove invertibility via high-order Taylor model methods to obtain rigorous lower bounds for the domains of definition of…

In this paper we study a class of dynamical systems generated by iterations of multivariate permutation polynomial systems which lead to polynomial growth of the degrees of these iterations. Using these estimates and the same techniques…

In this work we obtain recurrent formulae for the number of permutations with either increasing or monotonic (i.e., both increasing and decreasing) runs of bounded length. Our formulae allow one to efficiently compute the number of such…

We compute the generating functions of a O(n) model (loop gas model) on a random lattice of any topology. On the disc and the cylinder, they were already known, and here we compute all the other topologies. We find that the generating…

We study a process of generating random positive integer weight sequences $\{ W_n \}$ where the gaps between the weights $\{ X_n = W_n - W_{n-1} \}$ are i.i.d. positive integer-valued random variables. We show that as long as the gap…

Time evolution equations for dynamical systems can often be derived from generating functionals. Examples are Newton's equations of motion in classical dynamics which can be generated within the Lagrange or the Hamiltonian formalism. We…

Random matrix products arise in many science and engineering problems. An efficient evaluation of its growth rate is of great interest to researchers in diverse fields. In the current paper, we reformulate this problem with a generating…

We define matrix models that converge to the generating functions of a wide variety of loop models with fugacity taken in sets with an accumulation point. The latter can also be seen as moments of a non-commutative law on a subfactor planar…

It is well known that the behaviour of a branching process is completely described by the generating function of the offspring law and its fixed points. Branching random walks are a natural generalization of branching processes: a branching…

For a given permutation or set partition there is a natural way to assign a genus. Counting all permutations or partitions of a fixed genus according to cycle lengths or block sizes, respectively, is the main content of this article. After…

We discuss a method for computing the generating function for the multiplicity distribution in field theories with strong time dependent external sources. At leading order, the computation of the generating function reduces to finding a…

Certain families of combinatorial objects admit recursive descriptions in terms of generating trees: each node of the tree corresponds to an object, and the branch leading to the node encodes the choices made in the construction of the…

The random map model is a deterministic dynamical system in a finite phase space with n points. The map that establishes the dynamics of the system is constructed by randomly choosing, for every point, another one as being its image. We…

In a recent article a generalization of the binomial distribution associated with a sequence of positive numbers was examined. The analysis of the nonnegativeness of the formal expressions was a key-point to allow to give them a statistical…