Polynomials of Binomial Type and Lucas' Theorem
Number Theory
2014-12-11 v2
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.
Keywords
Cite
@article{arxiv.1412.1761,
title = {Polynomials of Binomial Type and Lucas' Theorem},
author = {David Goss},
journal= {arXiv preprint arXiv:1412.1761},
year = {2014}
}
Comments
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