In this paper, we consider the relationships between the second order linear recurrences and the permanents and determinants of tridiagonal matrices. 1. Introduction The well-known Fibonacci, Lucas and Pell numbers can be generalized as follows: Let A and B be nonzero, relatively prime integers such that D = A 4B 6= 0: De…ne sequences fung and fvng by, for all n 2 (see [10]), un = Aun 1 Bun 2 (...

While in the univariate case solutions of linear recurrences with constant coeecients have rational generating functions, we show that the multivariate case is much richer: even though initial conditions have rational generating functions, the corresponding solutions can have generating functions which are algebraic but not rational, D-nite but not algebraic, and even non D-nite.

This paper reports on the articulatory and acoustic correlates of the mid-central vowel (schwa) in an attempt to find out the perimeter of this vowel in both the articulatory and acoustic vowel space of female American English speakers. F1xF2 plots were used to determine the acoustic vowel space. The articulatory vowel space was determined by plotting the maximum vertical displacement of the ja...

In this paper, we find an explicit formulas, or recurrences, in terms of generating functions for the cardinalities of the sets Sn(T ; τ) of all permutations in Sn that contain τ ∈ Sk exactly once and avoid a subset T ⊆ S3 where |T | ≥ 2.

In recent work on multivariate elliptic hypergeometric integrals, the author generalized a conjectural integral formula of van Diejen and Spiridonov to a ten parameter integral provably invariant under an action of the Weyl group E7. In the present note, we consider the action of the affine Weyl group, or more precisely, the recurrences satisfied by special cases of the integral. These are of t...

Consider lattice paths in Z 2 with three step types: the up diagonal (1; 1), the down diagonal (1; ?1), and the double horizontal (2; 0). For n 1, let S n denote the set of such paths running from (0; 0) to (2n; 0) and remaining strictly above the x-axis except initially and terminally. It is well known that the cardinalities, r n = jS n j, are the large Schrr oder numbers. We use lattice paths...

Orthogonal polynomials on the unit circle are completely determined by their reflection coefficients through the Szegő recurrences. We assume that the reflection coefficients tend to some complex number a with 0 < |a| < 1. The orthogonality measure μ then lives essentially on the arc {e : α ≤ t ≤ 2π − α} where sin α 2 def = |a| with α ∈ (0, π). Under the certain rate of convergence it was prove...

Electrocardiogram (ECG) signals are analysed using the nonlinear method of recurrence plots, which reveals subtle time correlations in time-domain signals. Large-scale features in the recurrence plots, which consist entirely of single dots, line segments of different orientations and white spaces, are directly related to time-domain features in the original signals. The relationship between rec...

We consider a relatively new combinatorial structure called staircase tableaux. They were introduced in the context of the asymmetric exclusion process and Askey–Wilson polynomials; however, their purely combinatorial properties have gained considerable interest in the past few years. We will be interested in a general model of staircase tableaux in which symbols that appear in staircase tablea...

In this article, we propose a novel method for detecting environmental changes in the reinforcement learning. The proposed method utilizes recurrence plots of state transitions of the system, and quantifies changes of the recurrence plot by a texture analysis. It is shown that the proposed method is effective to detect environmental changes.