A bijection between 3-Motzkin paths and Schröder paths with no peak at odd.
A bijection between atomic partitions and unsplitable partitions.
A bijection between classes of fully packed loops and plane partitions.
A bijection on Dyck paths and its cycle structure.
A bijective proof of Borchardt's identity.
A binomial coefficient identity associated to a conjecture of Beukers.
A binomial coefficient identity associated with Beukers' conjecture on Apéry numbers.
A closer look at some new identities.
A colorful involution for the generating function for signed Stirling numbers of the first kind.
A combinatorial approach to partitions with parts in the gaps
Many links exist between ordinary partitions and partitions with parts in the “gaps”. In this paper, we explore combinatorial explanations for some of these links, along with some natural generalizations. In particular, if we let be the number of partitions of n into j parts where each part is ≡ k (mod m), 1 ≤ k ≤ m, and we let be the number of partitions of n into j parts where each part is ≡ k (mod m) with parts of size k in the gaps, then .
A combinatorial identity arising from cobordism theory.
A combinatorial interpretation for an identity of Barrucand.
A combinatorial proof of a result from number theory.
A combinatorial proof of a symmetric -Pfaff-Saalschütz identity.
A combinatorial proof of Sun's “curious” identity.
A combinatorial proof of the sum of -cubes.
A common generalization of binomial coefficients, Stirling numbers and Gaussian coefficients.
A common generalization of binomial coefficients, Stirling numbers and Gaussian Coefficientes
A common generalization of some identities.
A curious identity involving binomial coefficients.