The semigroup of fully indecomposable relations and Hall relations
The sequential join of combinatorial games.
The shape of a typical boxed plane partition.
The size of Fulton's essential set.
The size of Fulton's essential set.
The size of the largest part of random plane partitions of large integers.
The skew and relative derangements of type B.
The spt-crank for overpartitions
Bringmann, Lovejoy, and Osburn (2009, 2010) showed that the generating functions of the spt-overpartition functions , , , and M2spt(n) are quasimock theta functions, and satisfy a number of simple Ramanujan-like congruences. Andrews, Garvan, and Liang (2012) defined an spt-crank in terms of weighted vector partitions which combinatorially explain simple congruences modulo 5 and 7 for spt(n). Chen, Ji, and Zang (2013) were able to define this spt-crank in terms of ordinary partitions. In this...
The structure of standard modules, I: Universal algebras and the Rogers-Ramanujan identities.
The -analogs of secant and tangent numbers.
The -stability number of a random graph.
The tangent function and power residues modulo primes
Let be an odd prime, and let be an integer not divisible by . When is a positive integer with and is an th power residue modulo , we determine the value of the product , where In particular, if with , then
The tenacity of zero-one laws.
The triple, quintuple and setuple product identities revisited.
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.
The visibility parameter for words and permutations
We investigate the visibility parameter, i.e., the number of visible pairs, first for words over a finite alphabet, then for permutations of the finite set {1, 2, …, n}, and finally for words over an infinite alphabet whose letters occur with geometric probabilities. The results obtained for permutations correct the formula for the expectation obtained in a recent paper by Gutin et al. [Gutin G., Mansour T., Severini S., A characterization of horizontal visibility graphs and combinatorics on words,...
The weighted hook length formula. III: Shifted tableaux.