239 research outputs found
Ranks For Two Partition Quadruple Functions
Recently the author introduced two new integer partition quadruple functions,
which satisfy Ramanujan-type congruences modulo , , , and . Here
we reprove the congruences modulo , , and by defining a rank-type
statistic that gives a combinatorial refinement of the congruences
Some Smallest Parts Functions from Variations of Bailey's Lemma
We construct new smallest parts partition functions and smallest parts crank
functions by considering variations of Bailey's Lemma and conjugate Bailey
pairs. The functions we introduce satisfy simple linear congruences modulo
and . We introduce and give identities for two four variable
-hypergeometric functions; these functions specialize to some of our new
spt-crank-type functions as well as many known spt-crank-type functions
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