On the effect of variable identification on the essential arity of functions

Details On the effect of variable identification on the essential arity of functions On the effect of variable identification on the essential arity of functions

2007-01-11

arxiv.org/abs/math/0701332v1

Mathematics

Combinatorics

10 pages

Scientific paper

We show that every function of several variables on a finite set of k elements with n>k essential variables has a variable identification minor with at least n-k essential variables. This is a generalization of a theorem of Salomaa on the essential variables of Boolean functions. We also strengthen Salomaa's theorem by characterizing all the Boolean functions f having a variable identification minor that has just one essential variable less than f.

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