On a problem of Davenport and Schinzel
On a problem of R.L.Graham
On a problem of Steinhaus concerning binary sequences.
On a question of K. Leeb
On a restricted -non-squashing partition function.
On a septuple product identity.
On A System Of All Maximal Chains (Antichains) Of A Graph
On a theorem of Landau. (Sur un théorème de Landau.)
On a Two-Dimensional Search Problem
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 a uniformly integrable family of polynomials defined on the unit interval.
On an expansion theorem in the finite operator calculus of G.-C. Rota.
On an extension of Euler numbers and records of alternating permutations. (Sur une extension des nombres d'Euler et les records des permutations alternantes.)
On an extremal characterization of partitions
On an identity for the cycle indices of rooted tree automorphism groups.
On an integer sequence related to a product of trigonometric functions, and its combinatorial relevance.
On an open problem of Green and Losonczy: exact enumeration of freely braided permutations.
On another extension of -Pfaff-Saalschütz formula
In this paper we give an extension of -Pfaff-Saalschütz formula by means of Andrews-Askey integral. Applications of the extension are also given, which include an extension of -Chu-Vandermonde convolution formula and some other -identities.
On Arrangements of Jordan Arcs with Three Intersections per Pair.
On automatic infinite permutations∗
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
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...