Weighted partition rank and crank moments. III. A list of Andrews–Beck type congruences modulo 5, 7, 11 and 13

Abstract

Let [Formula: see text] count the total number of parts among partitions of [Formula: see text] with rank congruent to [Formula: see text] modulo [Formula: see text] and let [Formula: see text] count the total appearances of ones among partitions of [Formula: see text] with crank congruent to [Formula: see text] modulo [Formula: see text]. We provide a list of over 70 congruences modulo [Formula: see text], [Formula: see text], [Formula: see text] and [Formula: see text] involving [Formula: see text] and [Formula: see text], which are known as congruences of Andrews–Beck type. Some recent conjectures of Chan, Mao and Osburn are also included in this list.

Topics & Concepts