Polynomials of binomial type and Lucas’ Theorem

Goss, David

doi:10.1090/proc/12849

Polynomials of binomial type and Lucas’ Theorem
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Proc. Amer. Math. Soc. 144 (2016), 1897-1904 Request permission

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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