A combinatorial proof of Andrews’ partition functions related to Schur’s partition theorem

A Combinatorial Proof of Andrews’ Partition Functions Related to Schur’s Partition Theorem

We construct an involution to show equality between partition functions related to Schur’s second partition theorem.

A Combinatorial Proof of Andrews' Smallest Parts Partition Function

We give a combinatorial proof of Andrews' smallest parts partition function with the aid of rooted partitions introduced by Chen and the author.

A Bijective Proof of the Alladi-Andrews-Gordon Partition Theorem

Based on the combinatorial proof of Schur’s partition theorem given by Bressoud, and the combinatorial proof of Alladi’s partition theorem given by Padmavathamma, Raghavendra and Chandrashekara, we obtain a bijective proof of a partition theorem of Alladi, Andrews and Gordon.

Proof of Andrews' Conjecture on Partition Identities

A Generalisation of a Partition Theorem of Andrews to Overpartitions

A partition of n is a non-increasing sequence of natural numbers whose sum is n. An overpartition of n is a partition of n in which the first occurrence of a number may be overlined. For example, there are 14 overpartitions of 4: 4, 4, 3 + 1, 3 + 1, 3 + 1, 3 + 1, 2 + 2, 2 + 2, 2 + 1 + 1, 2 + 1 + 1, 2 + 1 + 1, 2 + 1 + 1, 1 + 1 + 1 + 1 and 1 + 1 + 1 + 1. In 1926, Schur [15] proved the following p...