A note on the -Genocchi numbers and polynomials.
A note on the Rogers-Fine identity.
A -analogue of a formula of Frobenius.
A partition identity with certain applications
A partition of R in two homogeneous and homeomorphic parts
A partition of the Catalan numbers and enumeration of genealogical trees
A special relational structure, called genealogical tree, is introduced; its social interpretation and geometrical realizations are discussed. The numbers of all abstract genealogical trees with exactly n+1 nodes and k leaves is found by means of enumeration of code words. For each n, the form a partition of the n-th Catalan numer Cₙ, that means .
A partition theorem for α-large sets
A permutation regularity lemma.
A permutations representation that knows what “Eulerian” means.
A Pivoting Algorithm for Convex Hulls and Vertex Enumeration of Arrangements and Polyhedra.
A probabilistic approach to the asymptotics of the length of the longest alternating subsequence.
A problem of Schur and its generalizations
A proof of a conjecture of Knuth.
A proof of the identities of Gordon and MacMahon and two new identities. (La démonstration des identités de Gordon et MacMahon et de deux identités nouvelles.)
A -analogue of an inequality due to Konrad Knopp.
A -analogue of Faulhaber's formula for sums of powers.
A -analogue of Graham, Hoffman and Hosoya's theorem.
A q-analogue of complete monotonicity
The aim of this paper is to give a q-analogue for complete monotonicity. We apply a classical characterization of Hausdorff moment sequences in terms of positive definiteness and complete monotonicity, adapted to the q-situation. The method due to Maserick and Szafraniec that does not need moments turns out to be useful. A definition of a q-moment sequence appears as a by-product.
A q-analogue of Lehmer's congruence
A quantum field theoretical representation of Euler-Zagier sums.