12 Large singularities of analytic functions 113 12.1 The saddle point 13 Multivariate generating functions 128 14 Mellin and other integral transforms 134 15 Functional equations, recurrences, and combinations of methods 137 15.1 Implicit functions, graphical enumeration, and related

In this work we introduce the triangular arrays of depth greater than 1 given by linear recurrences, that generalize some well-known recurrences that appear in enumerative combinatorics. In particular, we focussed on triangular arrays of depth 2, since they are closely related to the solution of linear three–term recurrences. We show through some simple examples how these triangular arrays appe...

Let K be a field of positive characteristic. When V is a linear variety in K and G is a finitely generated subgroup of K∗, we show how to compute the set V ∩ G effectively using heights. We calculate all the estimates explicitly. A special case provides the effective solution of the S-unit equation in n variables. 2000 MSC codes. 11D04, 11D72, 11G35, 11G50, 14G25.

This work provides a study on the multidistribution of type B excedances, fixed points and cycles on the permutations of type B. We derive the recurrences and closed formulas for the distribution of signed excedances on type B permutations as well as derangements via combinatorial construction. Based on this result, we obtain the recurrence and generating function for the signed excedance polyn...

We show the relationships between the determinants and permanents of certain tridiagonal matrices and the negatively subscripted terms of second-order linear recurrences.Also considering how to the negatively subscripted terms of second-order linear recurrences can be connected to Chebyshev polynomials by determinants of these matrices, we give factorizations and representations of these number...

In this paper, we give fourth order recurrences and generating matrices for the weighted sums of second order recurrences. We derive by matrix methods some new explicit formulas and combinatorial representations, and some relationships between the permanents of certain superdiagonal matrices and these sums.

ordering of the parts then this number reduces to the classical Stirling number of the second kind (see [3], p. 244). Often it is the case where there is a constraint on the size of the parts. For instance, consider ordered m-partitions of n where each part must be of size between 1 and N for some constant N ≥ 1. There are known recurrences for the number of such constrained ordered partitions ...

We use recurrences (alias difference equations) to prove that the two most important permutation statistics, namely the number of inversions and the major index, are asymptotically joint-independently-normal. We even derive more-precise-than-needed asymptotic formulas for the (normalized) mixed moments.

Recurrence quantification analysis (RQA)was used to analyse force signals during sustained sub-maximal grip contraction (SSGC) of three types of patients suffering from a metabolic muscle disorder (glycogen storage disease type III (GSD III), glycogen storage disease type V (GSD V) andmitochondrial myopathies (MITO)) compared to control subjects. Recurrence plots (RP) of patients showed clear n...

This paper closes an algorithmic problem of summing a set of mutual recurrence relations with constant coefficients. Given an order d system of the form A(n) = ∑d i=1 MiA(n− i)+G(n), where A,G : N→ Km and M1, . . . ,Md ∈Mm(K) for some field K and natural number m, this algorithm computes the sum ∑n i=0 A(i) as a K-linear combination of A(n), . . . , A(n − d), the initial conditions and sums of ...