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Displaying 1121 – 1140 of 2016

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On a Two-Dimensional Search Problem

Kolev, Emil, Landgev, Ivan (1995)

Serdica Mathematical Journal

In this article we explore the so-called two-dimensional tree− search problem. We prove that for integers m of the form m = (2^(st) − 1)/(2^s − 1) the rectangles A(m, n) are all tight, no matter what n is. On the other hand, we prove that there exist infinitely many integers m for which there is an infinite number of n’s such that A(m, n) is loose. Furthermore, we determine the smallest loose rectangle as well as the smallest loose square (A(181, 181)). It is still undecided whether there exist...

On another extension of q -Pfaff-Saalschütz formula

Mingjin Wang (2010)

Czechoslovak Mathematical Journal

In this paper we give an extension of q -Pfaff-Saalschütz formula by means of Andrews-Askey integral. Applications of the extension are also given, which include an extension of q -Chu-Vandermonde convolution formula and some other q -identities.

On automatic infinite permutations∗

Anna Frid, Luca Zamboni (2012)

RAIRO - Theoretical Informatics and Applications

An infinite permutation α is a linear ordering of N. We study properties of infinite permutations analogous to those of infinite words, and show some resemblances and some differences between permutations and words. In this paper, we try to extend to permutations the notion of automaticity. As we shall show, the standard definitions which are equivalent in the case of words are not equivalent in the context of permutations. We investigate the relationships...

On automatic infinite permutations

Anna Frid, Luca Zamboni (2012)

RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications

An infinite permutation α is a linear ordering of N. We study properties of infinite permutations analogous to those of infinite words, and show some resemblances and some differences between permutations and words. In this paper, we try to extend to permutations the notion of automaticity. As we shall show, the standard definitions which are equivalent in the case of words are not equivalent in the context of permutations. We investigate the relationships between these definitions and prove that...

On automatic infinite permutations∗

Anna Frid, Luca Zamboni (2012)

RAIRO - Theoretical Informatics and Applications

An infinite permutation α is a linear ordering of N. We study properties of infinite permutations analogous to those of infinite words, and show some resemblances and some differences between permutations and words. In this paper, we try to extend to permutations the notion of automaticity. As we shall show, the standard definitions which are equivalent in the case of words are not equivalent in the context of permutations. We investigate the relationships...

On averages of randomized class functions on the symmetric groups and their asymptotics

Paul-Olivier Dehaye, Dirk Zeindler (2013)

Annales de l’institut Fourier

The second author had previously obtained explicit generating functions for moments of characteristic polynomials of permutation matrices ( n points). In this paper, we generalize many aspects of this situation. We introduce random shifts of the eigenvalues of the permutation matrices, in two different ways: independently or not for each subset of eigenvalues associated to the same cycle. We also consider vastly more general functions than the characteristic polynomial of a permutation matrix, by...

On binary trees and Dyck paths

A. Panayotopoulos, A. Sapounakis (1995)

Mathématiques et Sciences Humaines

A bijection between the set of binary trees with n vertices and the set of Dyck paths of length 2n is obtained. Two constructions are given which enable to pass from a Dyck path to a binary tree and from a binary tree to a Dyck path.

On binary trees and permutations

A. Panayotopoulos, A. Sapounakis (1992)

Mathématiques et Sciences Humaines

Every binary tree is associated to a permutation with repetitions, which determines it uniquely. Two operations are introduced and used for the construction of the set of all binary trees. The set of all permutations which correspond to a given binary tree is determined and its cardinal number is evaluated.

On certain generalized q-Appell polynomial expansions

Thomas Ernst (2015)

Annales UMCS, Mathematica

We study q-analogues of three Appell polynomials, the H-polynomials, the Apostol-Bernoulli and Apostol-Euler polynomials, whereby two new q-difference operators and the NOVA q-addition play key roles. The definitions of the new polynomials are by the generating function; like in our book, two forms, NWA and JHC are always given together with tables, symmetry relations and recurrence formulas. It is shown that the complementary argument theorems can be extended to the new polynomials as well as to...

Currently displaying 1121 – 1140 of 2016