arXiv subjects

F. Jouhet

Publications and source records attributed to F. Jouhet.

6 recordsLinked to original sources

arXiv2022

Cyclotomic valuation of $q$-Pochhammer symbols and $q$-integrality of basic hypergeometric series

We give a formula for the cyclotomic valuation of $q$-Pochhammer symbols in terms of (generalized) Dwork maps. We also obtain a criterion for the $q$-integrality of basic hypergeometric series in terms of certain step functions, which generalize Christol step functions. This provides suitable $q$-analogs of two results proved by Christol: a formula for the $p$-adic valuation of Pochhammer symbols and a criterion for the $N$-integrality of hypergeometric series.

math.NT↗

arXiv2006

A generalization of Kawanaka's identity for Hall-Littlewood polynomials and applications

An infinite summation formula of Hall-Littlewood polynomials due to Kawanaka is generalized to a finite summation formula, which implies, as applications, twelve multiple q-identities of Rogers-Ramanujan type.

math.CO↗

arXiv2005

Some more semi-finite forms of bilateral basic hypergeometric series

We prove some new semi-finite forms of bilateral basic hypergeometric series. One of them yields in a direct limit Bailey's celebrated ${}_6ψ_6$ summation formula, answering a question recently raised by Chen and Fu ({\em Semi-Finite Forms of Bilateral Basic Hypergeometric Series}, Proc. Amer. Math. Soc., to appear).

math.CO↗

arXiv2003

Sur une generalisation des coefficients binomiaux

We prove a recent conjecture of Lassalle about positivity and integrality of coefficients in some polynomial expansions. We also give a combinatorial interpretation of those numbers. Finally, we show that this question is closely related to the fundamental problem of calculating the linearization coefficients for binomial coefficients.

math.CO↗

arXiv2001

New Identities of Hall-Littlewood Polynomials and Rogers-Ramanujan Type

We prove two new summation formulae of Hall-Littlewood polynomials over partitions into bounded parts and derive some new multiple $q$-identities of Rogers-Ramanujan type.

math.CO↗

arXiv2000

Some new identities for Schur functions

Some new identities for Schur functions are proved. In particular, we settle in the affirmative a recent conjecture of Ishikawa-Wakayama and solve a problem raised by Bressoud.

math.CO↗