A bijective proof of the hook-content formula for super Schur functions and a modified jeu de taquin.
A class of finite -series - II
A class of finite -series. - III
A closer look at some new identities.
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 proof of Andrews' smallest parts partition function.
A combinatorial proof of the sum of -cubes.
A connection between ordinary partitions and tilings with dominoes and squares.
A discontinuity in the distribution of fixed point sums.
A generalization of an Euler formula in partition theory
A note on partitions and compositions defined by inequalities.
A note on some polynomial identities
A note on the exact expected length of the th part of a random partition.
A partition identity with certain applications
A partition problem of Frobenius, II
A proof of the mock theta conjectures.
A simple proof of the Ramanujan conjecture for powers of 5.
Affine Lie algebras and modular forms
An application of Pólya’s enumeration theorem to partitions of subsets of positive integers
Let be a non-empty subset of positive integers. A partition of a positive integer into is a finite nondecreasing sequence of positive integers in with repetitions allowed such that . Here we apply Pólya’s enumeration theorem to find the number of partitions of into , and the number of distinct partitions of into . We also present recursive formulas for computing and .
An asymptotic formula in the theory of compositions.