Related papers: Introducing irrational enumeration: analytic combi…

We treat the problem of normally ordering expressions involving the standard boson operators a, a* where [a,a*]=1. We show that a simple product formula for formal power series - essentially an extension of the Taylor expansion - leads to a…

We generalize Khintchine's method of constructing totally irrational singular vectors and linear forms. The main result of the paper shows existence of totally irrational vectors and linear forms with large uniform Diophantine exponents on…

In this work we consider two different aspects of weighted walks in cones. To begin we examine a particular weighted model, known as the Gouyou-Beauchamps model. Using the theory of analytic combinatorics in several variables we obtain the…

We extend Robertson's theorem to apply to frames generated by the action of a discrete, countable abelian unitary group. Within this setup we use Stone's theorem and the theory of spectral multiplicity to analyze wandering frame…

We enumerate rational curves in toric surfaces passing through points and satisfying cross-ratio constraints using tropical and combinatorial methods. Our starting point is arXiv:1509.07453, where a tropical-algebraic correspondence theorem…

We obtain strong information on the asymptotic behaviour of the counting function for nilpotent Galois extensions with bounded discriminant of arbitrary number fields. This extends previous investigations for the case of abelian groups. In…

In these lectures three different methods of computing the asymptotic expansion of a Hermitian matrix integral is presented. The first one is a combinatorial method using Feynman diagrams. This leads us to the generating function of the…

The incomplete tribonacci polynomials, denoted by T_n^{(s)}(x), generalize the usual tribonacci polynomials T_n(x) and were introduced in [10], where several algebraic identities were shown. In this paper, we provide a combinatorial…

We introduce a Dirichlet-series framework for studying the asymptotic behavior of generalized factorial functions defined by Legendre-type valuation formulas. Let $K$ be a number field and let $S$ be a finite set of prime ideals. For a…

For a commutative algebra which comes from a Zinbiel algebra the exponential series can be written without denominators. When lifted to dendriform algebras this new series satisfies a functional equation analogous to the…

In this paper we reformulate in a simpler way the combinatoric core of constructive quantum field theory We define universal rational combinatoric weights for pairs made of a graph and one of its spanning trees. These weights are nothing…

We prove an asymptotic analog of the classical Hurewicz theorem on mappings which lower dimension. This theorem allows us to find sharp upper bound estimates for the asymptotic dimension of groups acting on finite dimensional metric spaces…

A new approach to the problem of finding the asymptotical behaviour of large orders of semiclassical expansion is suggested. Asymptotics of high orders not only for eigenvalues, but also for eigenfunctions, are constructed. Thus, one can…

When asymptotically analysing the summatory function of a $q$-regular sequence in the sense of Allouche and Shallit, the eigenvalues of the sum of matrices of the linear representation of the sequence determine the "shape" (in particular…

Working with generating functions, the combinatorics of a recurrence relation can be expressed in a way that allows for more efficient calculation of the quantity. This is true of the Catalan numbers for an ordered binary tree…

We propose a categorical setting for the study of the combinatorics of rational numbers. We find combinatorial interpretation for the Bernoulli and Euler numbers and polynomials.

A general analytical method is developed for describing crossover phenomena of arbitrary nature. The method is based on the algebraic self-similar renormalization of asymptotic series, with control functions defined by crossover conditions.…

A natural connection between rational functions of several real or complex variables, and subspace collections is explored. A new class of function, superfunctions, are introduced which are the counterpart to functions at the level of…

In the paper we develop an approach to asymptotic normality through factorial cumulants. Factorial cumulants arise in the same manner from factorial moments, as do (ordinary) cumulants from (ordinary) moments. Another tool we exploit is a…

We explore methods for constructing normal forms of indecomposable quiver representations. The first part of the paper develops homological tools for recursively constructing families of indecomposable representations from indecomposables…