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Notes on Umemura polynomials
Annales de la Faculté des sciences de Toulouse : Mathématiques, Serie 6, Volume 29 (2020) no. 5, pp. 1091-1118.

We give a survey on special polynomials associated with algebraic solutions of the sixth Painlevé equation, and formulate a conjecture regarding a combinatorial formula for Umemura polynomials associated with a class of algebraic solutions of P VI with two discrete parameters.

Nous donnons un survol des polynômes spéciaux associés aux solutions algébriques de la sixième équation de Painlevé, et formulons une conjecture concernant une formule combinatoire pour les polynômes d’Umemura associés à une classe de solutions algébriques de P VI avec deux paramètres discrets.

Published online:
DOI: 10.5802/afst.1658
Classification: 33C45,  05E35,  34M55
Keywords: Umemura polynomial, Painlevé equation, Toda equation, special polynomial
Masatoshi Noumi 1

1 Department of Mathematics, Kobe University, Rokko, Kobe 657-8501, Japan
License: CC-BY 4.0
Copyrights: The authors retain unrestricted copyrights and publishing rights
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Masatoshi Noumi. Notes on Umemura polynomials. Annales de la Faculté des sciences de Toulouse : Mathématiques, Serie 6, Volume 29 (2020) no. 5, pp. 1091-1118. doi : 10.5802/afst.1658. https://afst.centre-mersenne.org/articles/10.5802/afst.1658/

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