The Number of Canalyzing Functions over Any Finite Set


In this paper, we extend the definition of Boolean canalyzing functions to the canalyzing functions of multi-state case. Namely, f:QnQ , 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.

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Y. Li, D. Murrugarra, J. Adeyeye and R. Laubenbacher, "The Number of Canalyzing Functions over Any Finite Set," Open Journal of Discrete Mathematics, Vol. 3 No. 3, 2013, pp. 130-136. doi: 10.4236/ojdm.2013.33024.

Conflicts of Interest

The authors declare no conflicts of interest.


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