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Abstract: In his seminal 1994 paper entitled "Enumerative combinatorics and coding theory", Shalom Eliahou proposes a theory/method to enumerate the values of a polynomial in n variables with non-negative integer coefficients, assumed on {-1,+1}^n. The method builds an associated binary linear code whose enumeration of certain weight suffices to answer the question. We shall present Eliahou's theory, as well as its application to the problem of enumerating Legendre pairs. For background in Legendre pairs, please consult the ICECA 2022 talk .

Zoom Link https://rutgers.zoom.us/j/94346444480 [password: The 20th Catalan number, alias (40)!/(20!*21!), alias 6564120420 ]