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.
A reciprocity theorem for domino tilings.
A recurrence relation for the “inv" analogue of -Eulerian polynomials.
A recursive relation for weighted Motzkin sequences.
A refinement of a partition theorem of Sellers.
A refinement of Cayley's formula for trees.
A refinement of the formula for -ary trees and the Gould-Vandermonde's convolution.
A relation between restricted and unrestricted weighted Motzkin paths.
A relationship between the major index for tableaux and the charge statistic for permutations.