Bijective proofs of parity theorems for partition statistics.
Binomial coefficient predictors.
Binomial sums via Bailey's cubic transformation
By employing one of the cubic transformations (due to W. N. Bailey (1928)) for the -series, we examine a class of -series. Several closed formulae are established by means of differentiation, integration and contiguous relations. As applications, some remarkable binomial sums are explicitly evaluated, including one proposed recently as an open problem.
Bounds for the counting function of the Jordan-Pólya numbers
A positive integer is said to be a Jordan-Pólya number if it can be written as a product of factorials. We obtain non-trivial lower and upper bounds for the number of Jordan-Pólya numbers not exceeding a given number .
Brownian motion and the generalized Catalan numbers.