The Fermat cubic, elliptic functions, continued fractions, and a combinatorial excursion

Details The Fermat cubic, elliptic functions, continued fractions, and a combinatorial excursion The Fermat cubic, elliptic functions, continued fractions, and a combinatorial excursion

2005-07-13

arxiv.org/abs/math/0507268v1

Mathematics

Combinatorics

44 pages; submitted to "Seminaire Lotharingien de Combinatoire" (journal), July 2005

Scientific paper

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 P\'olya 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{\c{c}}on.

Affiliated with

Also associated with

No associations

Rating

The Fermat cubic, elliptic functions, continued fractions, and a combinatorial excursion does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with The Fermat cubic, elliptic functions, continued fractions, and a combinatorial excursion, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and The Fermat cubic, elliptic functions, continued fractions, and a combinatorial excursion will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-295280