Counting transitive relations.
Counting upper interactions in Dyck paths.
Counting walks in a quadrant: a unified approach via boundary value problems
The aim of this article is to introduce a unified method to obtain explicit integral representations of the trivariate generating function counting the walks with small steps which are confined to a quarter plane. For many models, this yields for the first time an explicit expression of the counting generating function. Moreover, the nature of the integrand of the integral formulations is shown to be directly dependent on the finiteness of a naturally attached group of birational transformations...
Counting with groups and rings.
Coupon collecting with quotas.
Cycle index, weight enumerator, and Tutte polynomial.
Cycle peaks and partial derivatives. (Pics de cycles et dérivés partielles.)
Cyclic derangements.
Cyclic sieving phenomenon in non-crossing connected graphs.
Delannoy and tetrahedral numbers
We establish an identity between Delannoy numbers and tetrahedral numbers of arbitrary dimension.
Dénombrements de chemins dans soumis à contraintes
Derangement polynomials and excedances of type .
Derangements and Euler's difference table for .
Derivative polynomials, Euler polynomials, and associated integer sequences.
Descendants and ascendants in binary trees.
Descendants in heap ordered trees or a triumph of computer algebra.
Descents in noncrossing trees.
Determinant formulae for some tiling problems and application to fully packed loops
We present a number of determinant formulae for the number of tilings of various domains in relation with Alternating Sign Matrix and Fully Packed Loop enumeration.
Determinant identities and a generalization of the number of totally symmetric self-complementary plane partitions.
Determinantal generating functions of colored spanning forests.