Combinatorial Aspects of Elliptic Curves II: Relationship between Elliptic Curves and Chip-Firing Games on Graphs
| dc.creator | Musiker, Gregg | |
| dc.date | 2007-10-02 | |
| dc.date.accessioned | 2026-07-07T08:33:34Z | |
| dc.date.available | 2026-07-07T08:33:34Z | |
| dc.description | Let q be a power of a prime and E be an elliptic curve defined over F_q. In "Combinatorial aspects of elliptic curves" [17], the present author examined a sequence of polynomials which express the N_k's, the number of points on E over the field extensions F_{q^k}, in terms of the parameters q and N_1 = #E(F_q). These polynomials have integral coefficients which alternate in sign, and a combinatorial interpretation in terms of spanning trees of wheel graphs. In this sequel, we explore further ramifications of this connection. In particular, we highlight a relationship between elliptic curves and chip-firing games on graphs by comparing the groups structures of both. As a coda, we construct a cyclic rational language whose zeta function is dual to that of an elliptic curve. | |
| dc.description | 24 pages, 2 figures, part of author's Ph.D. Thesis, presented at FPSAC 2007 | |
| dc.identifier | https://arxiv.org/abs/0710.0574 | |
| dc.identifier | http://arxiv.org/abs/0710.0574 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/139179 | |
| dc.subject | Combinatorics | |
| dc.subject | Number Theory | |
| dc.subject | 11G07; 05C25 | |
| dc.title | Combinatorial Aspects of Elliptic Curves II: Relationship between Elliptic Curves and Chip-Firing Games on Graphs | |
| dc.type | text |