Name
Title | ||
|---|---|---|
Polyhedral geometry, supercranks, and combinatorial witnesses of congruences for partitions into three parts |
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 supercranks that combinatorially witness every instance of divisibility of p(n,3) by any prime m≡−1(mod6), 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′≡1(mod6) is also discussed. |
Year | DOI | Venue |
|---|---|---|
2017 | 10.1016/j.ejc.2017.06.002 | European Journal of Combinatorics |
Field | DocType | Volume |
Prime (order theory),Discrete mathematics,Combinatorics,Partition function (mathematics),Divisibility rule,Bijection, injection and surjection,Lattice (group),Geometry,Congruence relation,Mathematics | Journal | 65 |
Issue | ISSN | Citations |
C | 0195-6698 | 0 |
PageRank | References | Authors |
0.34 | 1 | 3 |
Name | Order | Citations | PageRank |
|---|---|---|---|
| Felix Breuer | 1 | 1 | 0.69 |
| Dennis Eichhorn | 2 | 0 | 0.68 |
| Brandt Kronholm | 3 | 0 | 0.34 |