ON ANDREWS’ PARTITION FUNCTION EO(n)
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Recently, Andrews introduced partition functions EO(n) and EO(n) where the function EO(n) denotes the number of partitions of n in which every even part is less than each odd part and the function EO(n) denotes the number of partitions enumerated by EO(n) in which only the largest even part appears an odd number of times. In this paper, we prove new congruences for EO(n) and pD(n), the number of partitions into distinct (or, odd) parts. We further establish linear recurrence relations for pD(n), which counts the number of partitions of n into distinct parts with 2 types of each part and EO(n).
Abstract
Recently, Andrews introduced partition functions EO(n) and EO(n) where the function EO(n) denotes the number of partitions of n in which every even part is less than each odd part and the function EO(n) denotes the number of partitions enumerated by EO(n) in which only the largest even part appears an odd number of times. In this paper, we prove new congruences for EO(n) and pD(n), the number of partitions into distinct (or, odd) parts. We further establish linear recurrence relations for pD(n), which counts the number of partitions of n into distinct parts with 2 types of each part and EO(n).
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