Towards characterising polynomiality of 1-qb1-qa[nm] and applications

Mohamed El Bachraoui

doi:10.1007/s11139-016-9877-y

Towards characterising polynomiality of 1-^qb1-^qa[nm] and applications

Mohamed El Bachraoui

Department of Mathematical Sciences

Research output: Contribution to journal › Article › peer-review

Abstract

In this note, we shall give conditions which guarantee that 1-qb1-qa[nm]∈Z[q] holds. We shall provide a full characterisation for 1-qb1-qa[kam]∈Z[q]. This unifies a variety of results already known in literature. We shall prove new divisibility properties for the binomial coefficients and a new divisibility result for a certain finite sum involving the roots of the unity.

Original language	English
Pages (from-to)	291-298
Number of pages	8
Journal	Ramanujan Journal
Volume	45
Issue number	1
DOIs	https://doi.org/10.1007/s11139-016-9877-y
Publication status	Published - Jan 1 2018

Keywords

Binomial coefficients
Divisibility
q-Binomial coefficients

ASJC Scopus subject areas

Algebra and Number Theory

Access to Document

10.1007/s11139-016-9877-y

Cite this

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abstract = "In this note, we shall give conditions which guarantee that 1-qb1-qa[nm]∈Z[q] holds. We shall provide a full characterisation for 1-qb1-qa[kam]∈Z[q]. This unifies a variety of results already known in literature. We shall prove new divisibility properties for the binomial coefficients and a new divisibility result for a certain finite sum involving the roots of the unity.",

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KW - Divisibility

KW - q-Binomial coefficients

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