Matthieu JosuatVergès ; JangSoo Kim

TouchardRiordan formulas, Tfractions, and Jacobi's triple product identity
dmtcs:2934 
Discrete Mathematics & Theoretical Computer Science,
January 1, 2011,
DMTCS Proceedings vol. AO, 23rd International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2011)

https://doi.org/10.46298/dmtcs.2934
TouchardRiordan formulas, Tfractions, and Jacobi's triple product identityArticle
Authors: Matthieu JosuatVergès ^{1}; JangSoo Kim ^{2}
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Matthieu JosuatVergès;JangSoo Kim
1 Fakultät für Mathematik [Wien]
2 School of Mathematics
We give a combinatorial proof of a TouchardRiordanlike 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 Tfractions, whose important property is the fact that they satisfy some functional equation. We show that this result permits to explain and generalize some TouchardRiordanlike formulas appearing in enumerative problems.