The Fermat cubic, elliptic functions, continued fractions, and a combinatorial excursion
| dc.creator | Conrad, Eric van Fossen | |
| dc.creator | Flajolet, Philippe | |
| dc.date | 2005-07-13 | |
| dc.date.accessioned | 2026-07-07T05:21:39Z | |
| dc.date.available | 2026-07-07T05:21:39Z | |
| dc.description | Elliptic functions considered by Dixon in the nineteenth century and related to Fermat's cubic, $x^3+y^3=1$, lead to a new set of continued fraction expansions with sextic numerators and cubic denominators. The functions and the fractions are pregnant with interesting combinatorics, including a special Pólya urn, a continuous-time branching process of the Yule type, as well as permutations satisfying various constraints that involve either parity of levels of elements or a repetitive pattern of order three. The combinatorial models are related to but different from models of elliptic functions earlier introduced by Viennot, Flajolet, Dumont, and Fran{ç}on. | |
| dc.description | 44 pages; submitted to "Seminaire Lotharingien de Combinatoire" (journal), July 2005 | |
| dc.identifier | https://arxiv.org/abs/math/0507268 | |
| dc.identifier | http://arxiv.org/abs/math/0507268 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/75771 | |
| dc.subject | Combinatorics | |
| dc.subject | Probability | |
| dc.subject | 05A15; 30B70; 33C75; 60C05 | |
| dc.title | The Fermat cubic, elliptic functions, continued fractions, and a combinatorial excursion | |
| dc.type | text |