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The Number of Canalyzing Functions over Any Finite Set

The Number of Canalyzing Functions over Any Finite Set
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摘要 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→∞. 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→∞.
出处 《Open Journal of Discrete Mathematics》 2013年第3期130-136,共7页 离散数学期刊(英文)
关键词 Canalyzing Function INCLUSION and EXCLUSION PRINCIPLE Canalyzing Function Inclusion and Exclusion Principle
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