@

author = {W.Y.C.Chen and D.D.M.Sang and Diane Y.H. Shi},}

title = {{ The Rogers-Ramanujan-Gordon theorem for overpartitions}},

language = {english},

abstract = {Let Bk,i(n) be the number of partitions of n with certain difference condition and let Ak,i(n) be the number of partitions of n with certain congruence condition. The Rogers–Ramanujan– Gordon theorem states that Bk,i(n) = Ak,i(n). Lovejoy obtained an overpartition analogue of the Rogers–Ramanujan–Gordon theorem for the cases i = 1 and i = k. We find an overpartition analogue of the Rogers–Ramanujan–Gordon theorem in the general case. Let Dk,i(n) be the number of overpartitions of n satisfying certain difference condition and Ck,i(n) be the number of overpartitions of n whose non-overlined parts satisfy certain congruence condition. We show that Ck,i(n) = Dk,i(n). By using a function introduced by Andrews, we obtain a recurrence relation that implies that the generating function of Dk,i(n) equals the generating function of Ck,i(n). By introducing the Gordon marking of an overpartition, we find a generating function formula for Dk,i(n) that can be considered an overpartition analogue of an identity of Andrews for ordinary partitions.},

journal = {Proceedings of the London Mathematical Society},

volume = {106},

number = {3},

pages = {1371--1393},

isbn_issn = {0024-6115},

year = {2013},

refereed = {yes},

length = {23}