The locality of words is a relatively young structural complexity measure, introduced by Day et al. in 2017 order to define classes patterns with variables which can be matched polynomial time. main tool used compute the word called marking sequence: an ordering distinct letters occurring respective order. Once sequence defined, are marked steps: i\(^{\text {th}}\) step, all occurrences letter ...

SUMMARY Classification tasks in computer vision and brain-computer interface research have presented several applications such as biometrics and cognitive training. However, like in any other discipline, determining suitable representation of data has been challenging, and recent approaches have deviated from the familiar form of one vector for each data sample. This paper considers a kernel be...

Let f be a piecewise analytic function on the unit interval (respectively, the unit circle of the complex plane). Starting from the Chebyshev (respectively, Fourier) coefficients of f , we construct a sequence of fast decreasing polynomials (respectively, trigonometric polynomials) which “detect” the points where f fails to be analytic, provided f is not infinitely differentiable at these points.

We show new lower bounds for the star-discrepancy and its inverse for subsets of the unit cube. They are polynomial in the quotient d/n of the number n of sample points and the dimension d. They provide the best known lower bounds for n not too large compared with d.

count ternary trees and the number of certain plane partitions and alternating sign matrices. Tamm evaluated these determinants by showing that the generating function for these entries has a continued fraction that is a special case of Gauss’s continued fraction for a quotient of hypergeometric series. We give a systematic application of the continued fraction method to a number of similar Han...

We study a family of orthogonal polynomials which generalizes a sequence of polynomials considered by L. Carlitz. We show that they are a special case of the Sheffer polynomials and point out some interesting connections with certain Sobolev orthogonal polynomials.

In hypercomplex context, we have recently constructed Appell sequences with respect to a generalized Laguerre derivative operator. This construction is based on the use of a basic set of monogenic polynomials which is particularly easy to handle and can play an important role in applications. Here we consider Laguerre-type exponentials of order m and introduce Laguerre-type circular and hyperbo...

This article describes conjectured combinatorial interpretations for the higher q, t-Catalan sequences introduced by Garsia and Haiman, which arise in the theory of symmetric functions and Macdonald polynomials. We define new combinatorial statistics generalizing those proposed by Haglund and Haiman for the original q, tCatalan sequence. We prove explicit summation formulas, bijections, and rec...

In this short note we focus on self-inverse Sheffer sequences and involutions in the Riordan group. We translate the results of Brown and Kuczma on self-inverse sequences of Sheffer polynomials to describe all involutions in the Riordan group.

A Barker sequence is a finite sequence of integers, each ±1, whose aperiodic autocorrelations are all as small as possible. It is widely conjectured that only finitely many Barker sequences exist. We describe connections between Barker sequences and several problems in analysis regarding the existence of polynomials with ±1 coefficients that remain flat over the unit circle according to some cr...