Counting nondecreasing integer sequences that Lie below a barrier.
Counting nonintersecting lattice paths with turns.
Counting non-isomorphic maximal independent sets of the -cycle graph.
Counting occurrences of 132 in an even permutation.
Counting ordered patterns in words generated by morphisms.
Counting pattern-free set partitions. II: Noncrossing and other hypergraphs.
Counting peaks and valleys in a partition of a set.
Counting peaks and valleys in -colored Motzkin paths.
Counting peaks at height in a Dyck path.
Counting polyominoes on twisted cylinders.
Counting rises, levels, and drops in compositions.
Counting segmented permutations using bicoloured Dyck paths.
Counting stabilized-interval-free permutations.
Counting subwords in a partition of a set.
Counting the number of elements in the mutation classes of -quivers.
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.