Counting lattice paths by Narayana polynomials.
Counting Maximal Distance-Independent Sets in Grid Graphs
Previous work on counting maximal independent sets for paths and certain 2-dimensional grids is extended in two directions: 3-dimensional grid graphs are included and, for some/any ℓ ∈ N, maximal distance-ℓ independent (or simply: maximal ℓ-independent) sets are counted for some grids. The transfer matrix method has been adapted and successfully applied
Counting multiderangements by excedances.
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 paths between points on a circle
The paper deals with counting sets of given magnitude whose elements are self-avoiding paths with nodes from a fixed set of points on a circle. Some of the obtained formulae provide new properties of entries in ``The On-line Encyclopaedia of Integer Sequences", while others generate new entries therein.
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 points of slope varieties over finite fields.
Counting polyominoes on twisted cylinders.
Counting rises, levels, and drops in compositions.
Counting rooted trees: the universal law .
Counting segmented permutations using bicoloured Dyck paths.
Counting set systems by weight.
Counting stabilized-interval-free permutations.