TITLE:
The Number of Canalyzing Functions over Any Finite Set
AUTHORS:
Yuan Li, David Murrugarra, John O. Adeyeye, Reinhard Laubenbacher
KEYWORDS:
Canalyzing Function; Inclusion and Exclusion Principle
JOURNAL NAME:
Open Journal of Discrete Mathematics,
Vol.3 No.3,
July
12,
2013
ABSTRACT: In this paper, we extend the
definition of Boolean canalyzing functions to the canalyzing functions of
multi-state case. Namely, f:Qn→Q , where Q={a1,a2,...,aq} . We obtain its cardinality
and the cardinalities of its various subsets (They may not be disjoint). When q=2, we obtain a combinatorial
identity by equating our result to the formula in [1]. For a better
understanding to the magnitude, we obtain the asymptotes for all the
cardinalities as either n→∞ or q→∞.