TY - JOUR
T1 - Arithmetic properties of partitions with odd parts distinct
AU - Hirschhorn, Michael D.
AU - Sellers, James Allen
PY - 2010/4/15
Y1 - 2010/4/15
N2 - In this work, we consider the function pod(n), the number of partitions of an integer n wherein the odd parts are distinct (and the even parts are unrestricted), a function which has arisen in recent work of Alladi. Our goal is to consider this function from an arithmetic point of view in the spirit of Ramanujan's congruences for the unrestricted partition function p(n). We prove a number of results for pod(n) including the following infinite family of congruences: for all α≥0 and n≥0.
AB - In this work, we consider the function pod(n), the number of partitions of an integer n wherein the odd parts are distinct (and the even parts are unrestricted), a function which has arisen in recent work of Alladi. Our goal is to consider this function from an arithmetic point of view in the spirit of Ramanujan's congruences for the unrestricted partition function p(n). We prove a number of results for pod(n) including the following infinite family of congruences: for all α≥0 and n≥0.
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U2 - 10.1007/s11139-010-9225-6
DO - 10.1007/s11139-010-9225-6
M3 - Article
AN - SCOPUS:77954862689
VL - 22
SP - 273
EP - 284
JO - Ramanujan Journal
JF - Ramanujan Journal
SN - 1382-4090
IS - 3
ER -