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On generating large classes of Sheffer functions

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Abstract

Let A be a finite set,n > 1 andD \( \subseteq \) A n. We say thatf:D → A is a partial Sheffer function of size |D| if eachf*: A n → A agreeing withf onD is Sheffer (or complete that is 〈A; f〉 primal), i.e. iff* generates allg:A m → A (m = 1, 2, ⋯) via repeated composition. The least size of a partial Sheffer function is shown to be |A| + 2 and all partial Sheffer functions of this size are exhibited. This shows how surprisingly little information onf is needed to ensure thatf is Sheffer and, at the same time, gives a description of large classes of Sheffer functions.

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Authors and Affiliations

  1. Centre de recherches mathématiques, Université de Montréal, Montréal, Québec, Canada

    I. G. Rosenberg

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  1. I. G. Rosenberg
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This work was supported by a grant from the Ministère de l'Education du Québec (programme “Formation de chercheurs et action concertée”).

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Rosenberg, I.G. On generating large classes of Sheffer functions. Aequat. Math. 17, 164–181 (1978). https://doi.org/10.1007/BF01818558

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