The number of inequivalent optimal covering codes.
The number of knight's tours equals 33, 439, 123, 484, 294—counting with binary decision diagrams.
The number of labeled 2-connected planar graphs.
The number of [old-time] basketball games with final score : where the home team was never losing but also never ahead by more than points.
The number of orthogonal Latin squares
The number of triangles formed by intersecting diagonals of a regular polygon.
The -adic valuations of sequences counting alternating sign matrices.
The Pfaffian transform.
The polynomial part of a restricted partition function related to the Frobenius problem.
The problem of kings.
The problem of the kings.
The -Bell numbers.
The ratio and generating function of cogrowth coefficients of finitely generated groups
Let G be a group generated by r elements . Among the reduced words in of length n some, say , represent the identity element of the group G. It has been shown in a combinatorial way that the 2nth root of has a limit, called the cogrowth exponent with respect to the generators . We show by analytic methods that the numbers vary regularly, i.e. the ratio is also convergent. Moreover, we derive new precise information on the domain of holomorphy of γ(z), the generating function associated...
The Redheffer matrix of a partially ordered set.
The size of Fulton's essential set.
The two-parameter class of Schröder inversions
Infinite lower triangular matrices of generalized Schröder numbers are used to construct a two-parameter class of invertible sequence transformations. Their inverses are given by triangular matrices of coordination numbers. The two-parameter class of Schröder transformations is merged into a one-parameter class of stretched Riordan arrays, the left-inverses of which consist of matrices of crystal ball numbers. Schröder and inverse Schröder transforms of important sequences are calculated.
The umbral transfer-matrix method. III: Counting animals.
The umbral transfer-matrix method. IV: Counting self-avoiding polygons and walks.
The umbral transfer-matrix method. V: The Goulden-Jackson cluster method for infinitely many mistakes.
Three-letter-pattern avoiding permutations and functional equations.