Notes on Umemura polynomials

— 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 PVI with two discrete parameters. RÉSUMÉ. — 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 PVI avec deux paramètres discrets.

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