@

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

title = {{An overpartition analogue of Bressoud’s theorem of Rogers-Ramanujan type}},

language = {english},

abstract = {For k≥2 and k≥i≥1, let Bk,i(n) denote the number of partitions of n such that part 1 appears at most i−1 times, two consecutive integers l and l+1 appear at most k−1 times, and if l and l+1 appear exactly k−1 times then the sum of the parts l and l+1 is congruent to i−1 modulo 2. Let Ak,i(n) denote the number of partitions with parts not congruent to 0, ±i modulo 2k. Bressoud’s theorem states that Ak,i(n)=Bk,i(n). Corteel, Lovejoy, and Mallet found an overpartition analogue of Bressoud’s theorem for i=1, that is, for overpartitions not containing non-overlined part 1. We obtain an overpartition analogue of Bressoud’s theorem in the general case. For k≥2 and k≥i≥1, let Dk,i(n) denote the number of overpartitions of n such that non-overlined part 1 appears at most i−1 times, for any integer l, l and non-overlined l+1 appear at most k−1 times, and if the parts l and non-overlined part l+1 together appear exactly k−1 times then the sum of the parts l and non-overlined parts l+1 has the same parity as the number of overlined parts that are less than l+1 plus i−1. Let Ck,i(n) denote the number of overpartitions of n with the non-overlined parts not congruent to ±i and 2k−1 modulo 2k−1. We show that Ck,i(n)=Dk,i(n). Note that this relation can also be considered as a Rogers–Ramanujan–Gordon type theorem for overpartitions.},

journal = {The Ramanujan Journal},

volume = {36},

number = {1},

pages = {69--80},

isbn_issn = {1382-4090},

year = {2015},

refereed = {yes},

length = {12}