Aequationes mathematicae

, Volume 17, Issue 1, pp 164–181

# On generating large classes of Sheffer functions

• I. G. Rosenberg
Research papers

## 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.

## AMS (1970) subject classification

Primary 08A25 Secondary 02C05

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