On the main diagonal of sheffer functions

✍ Scribed by J. Demetrovics

• Publisher: Elsevier Science
• Year: 1978
• Tongue: English
• Weight: 473 KB
• Volume: 21
• Category: Article
• ISSN: 0012-365X
• DOI: 10.1016/0012-365x(78)90142-5

✦ Synopsis

Necessary and sufi&nt conditions: far a one variable function to be the main diagonal of a Sbeffer function are given and estimates are obtained for the number of Sheffer furktwns.

Many papers [l-9] dealing with Sheffer functions have recently jypeared. In these papeij: the authors deal with criteria for a function to be a She&r function.

In Cl] and [4] the authors give general fo?ms for many Sheffer functions.

The present paper gives necessary and sufficient conditions for a function of one variable to be t'ie main diagonal of a Shefkr function. It also draws many conclusions concerning the multitude of Sheffer functions of k variables. Let &={O, 1,. . . , k -* 1). By a k-valued function we will mean a function f : E+ &. By a k-valued logic Pk we will mean the set of sufzh functions. Ckkler the sets Lo(f) = {f(x,, x2, . . . . x,)) U {x,, x2, . . . , xi, . . .) and L,+,(f) =