The Number of Canalyzing Functions over Any Finite Set ()
Yuan Li,
David Murrugarra,
John O. Adeyeye,
Reinhard Laubenbacher
Department of Mathematics, Winston-Salem State University, Winston-Salem, USA.
School of Mathematics, Georgia Tech, Atlanta, USA.
Virginia Bioinformatics Institute, Virginia Tech, Blacksburg, USA.
DOI: 10.4236/ojdm.2013.33024
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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→∞.
Share and Cite:
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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