Polynomials of binomial type and Lucas’ Theorem
Copyright policy )Polynomials of binomial type and Lucas’ Theorem
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.
- The Ohio State University United States
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
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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