Service interruption on Monday 11 July from 12:30 to 13:00: all the sites of the CCSD (HAL, EpiSciences, SciencesConf, AureHAL) will be inaccessible (network hardware connection).
Skip to Main content Skip to Navigation
Conference papers

Touchard-Riordan formulas, T-fractions, and Jacobi's triple product identity

Abstract : We give a combinatorial proof of a Touchard-Riordan-like formula discovered by the first author. As a consequence we find a connection between his formula and Jacobi's triple product identity. We then give a combinatorial analog of Jacobi's triple product identity by showing that a finite sum can be interpreted as a generating function of weighted Schröder paths, so that the triple product identity is recovered by taking the limit. This can be stated in terms of some continued fractions called T-fractions, whose important property is the fact that they satisfy some functional equation. We show that this result permits to explain and generalize some Touchard-Riordan-like formulas appearing in enumerative problems.
Complete list of metadata

Cited literature [10 references]  Display  Hide  Download
Contributor : Coordination Episciences Iam Connect in order to contact the contributor
Submitted on : Tuesday, October 13, 2015 - 3:05:45 PM
Last modification on : Friday, April 1, 2022 - 3:20:02 PM
Long-term archiving on: : Thursday, January 14, 2016 - 1:40:55 PM


Publisher files allowed on an open archive




Matthieu Josuat-Vergès, Jang-Soo Kim. Touchard-Riordan formulas, T-fractions, and Jacobi's triple product identity. 23rd International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2011), 2011, Reykjavik, Iceland. pp.563-574, ⟨10.46298/dmtcs.2934⟩. ⟨hal-01215053⟩



Record views


Files downloads