@

author = {Felix Breuer and Dennis Eichhorn and Brandt Kronholm},}

title = {{Polyhedral geometry, supercranks, and combinatorial witnesses of congruences for partitions into three parts}},

language = {english},

abstract = {In this paper, we use a branch of polyhedral geometry, Ehrhart theory, to expand our combinatorial understanding of congruences for partition functions. Ehrhart theory allows us to give a new decomposition of partitions, which in turn allows us to define statistics called {\it supercranks} that combinatorially witness every instance of divisibility of $p(n,3)$ by any prime $m \equiv -1 \pmod 6$, where $p(n,3)$ is the number of partitions of $n$ into three parts. A rearrangement of lattice points allows us to demonstrate with explicit bijections how to divide these sets of partitions into $m$ equinumerous classes. The behavior for primes $m' \equiv 1 \pmod 6$ is also discussed. },

year = {2015},

month = {August},

howpublished = {arXiv },

keywords = {Integer partitions, Polyhedral Geometry, Combinatorics, Freeman Dyson, Ramanujan, Ehrhart, Crank, Generating Function, },

length = {28},

type = {RISC Report Series},

institution = {Research Institute for Symbolic Computation (RISC), Johannes Kepler University Linz},

address = {Schloss Hagenberg, 4232 Hagenberg, Austria}