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Polynomials of binomial type and Lucas' Theorem


Author: David Goss
Journal: Proc. Amer. Math. Soc. 144 (2016), 1897-1904
MSC (2010): Primary 11G09, 11R58, 12E10; Secondary 05A10
DOI: https://doi.org/10.1090/proc/12849
Published electronically: September 9, 2015
MathSciNet review: 3460152
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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 have then accounted for all sequences in finite characteristic which satisfy the Binomial Theorem.


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Additional Information

David Goss
Affiliation: Department of Mathematics, The Ohio State University, 231 West $18^{th}$ Avenue, Columbus, Ohio 43210
Email: dmgoss@gmail.com

DOI: https://doi.org/10.1090/proc/12849
Received by editor(s): December 10, 2014
Received by editor(s) in revised form: May 27, 2015
Published electronically: September 9, 2015
Communicated by: Matthew A. Papanikolas
Article copyright: © Copyright 2015 American Mathematical Society