Abstract
Inspired by a number of recent papers by Corteel, Dousse, Foda, Uncu and Welsh on cylindric partitions and RogersâRamanujan-type identities, we obtain theA2\mathrm {A}_2(orA2(1)\mathrm {A}_2^{(1)}) analogues of the celebrated AndrewsâGordon identities. We further proveqq-series identities that correspond to the infinite-level limit of the AndrewsâGordon identities forArâ1\mathrm {A}_{r-1}(orArâ1(1)\mathrm {A}_{r-1}^{(1)}) for arbitrary rankrr. Our results forA2\mathrm {A}_2also lead to conjectural, manifestly positive, combinatorial formulas for the22-variable generating function of cylindric partitions of rank33and leveldd, such thatddis not a multiple of33.
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More From: Transactions of the American Mathematical Society, Series B
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