A combinatorial proof of the log-concavity of a famous sequence counting permutations.
A combinatorial proof of the sum of -cubes.
A combinatorial representation with Schröder paths of biorthogonality of Laurent biorthogonal polynomials.
A common generalization of binomial coefficients, Stirling numbers and Gaussian coefficients.
A common generalization of binomial coefficients, Stirling numbers and Gaussian Coefficientes
A common generalization of some identities.
A common generating function for Catalan numbers and other integer sequences.
A complete categorization of when generalized Tribonacci sequences can be avoided by additive partitions.
A complete grammar for decomposing a family of graphs into 3-connected components.
A conjecture of Stanley on alternating permutations.
A conjectured formula for fully packed loop configurations in a triangle.
A continued fraction expansion for a -tangent function.
A Contribution to the Theory of Permutations
A criterion for unimodality.
A curious identity involving binomial coefficients.
A de Bruijn-type formula for enumerating patterns of partitions.
A density version of the Carlson–Simpson theorem
We prove a density version of the Carlson–Simpson Theorem. Specifically we show the following. For every integer and every set of words over satisfying there exist a word over and a sequence of left variable words over such that the set is contained in . While the result is infinite-dimensional its proof is based on an appropriate finite and quantitative version, also obtained in the paper.
A determinant identity that implies Rogers-Ramanujan.
A determinant of the Chudnovskys generalizing the elliptic Frobenius-Stickelberger-Cauchy determinantal identity.
A different -analogue of Euler numbers. (Un autre -analogue des nombres d'Euler.)