Polynomials of binomial type and Lucas’ Theorem

descriptionPublicationkeyboard_double_arrow_right Article , Preprint , Other literature type 09 Sep 2015Embargo end date: 01 Jan 2014 English Publisher:American Mathematical Society (AMS)Journal:Proceedings of the American Mathematical Society, volume 144, pages 1,897-1,904 (issn: 0002-9939, eissn: 1088-6826,

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Authors: Goss, David;

doi: 10.1090/proc/12849 , 10.48550/arxiv.1412.1761

arXiv: 1412.1761

Polynomials of binomial type and Lucas’ Theorem

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Abstract

We present various constructions of sequences of polynomials satisfying the Binomial Theorem in finite characteristic based on the theory of additive polynomials. Various actions on these constructions are also presented. It is an open question whether we then have accounted for all sequences in finite characteristic which satisfy the Binomial Theorem.

At the intersection of number theory, commutative algebra and combinatorics. The new version has additional references. ALSO, it includes an umbral construction of the Carlitz module pointed out to us by F. Pellarin

Related Organizations

The Ohio State University
United States

Keywords

binomial type, Carlitz construction, Arithmetic theory of algebraic function fields, Lucas' congruence, Mathematics - Number Theory, additive polynomials, FOS: Mathematics, Special polynomials in general fields, Number Theory (math.NT), Drinfel'd modules; higher-dimensional motives, etc., Factorials, binomial coefficients, combinatorial functions

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