The Number of Canalyzing Functions over Any Finite Set

• 作者: David Murrugarra John O. Adeyeye Reinhard Laubenbacher Yuan Li
• 来源期刊: 离散数学期刊(英文)
• 学科: 数学
• 关键词: Canalyzing Function INCLUSION and EXCLUSION PRINCIPLE
• 年，卷（期）: 2013,（3）
• 页码范围: 130-136
• 页数: 7页
• 分类号: O1

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→∞.