具有非平凡arity间隙的有限对称函数
Finite symmetric functions with non-trivial arity gap
摘要：
给定一个$n$元$k-$值函数$f$，$gap(f)$表示$f$的本质元间隙，它是当识别$f$中的任何两个不同的本质变量时，$f$中变为虚拟的本质变量的最小数目.本文研究了具有非平凡元间隙的对称函数（$2\leq gap(f)$）的性质.我们证明了关于具有非平凡元间隙的对称函数与其子函数或子函数的分解的几个结果。证明了具有非平凡间隔的对称函数的本质变量的所有非空集合都是可分的。
英文摘要：
Given an $n$-ary $k-$valued function $f$, $gap(f)$ denotes the essential arity gap of $f$ which is the minimal number of essential variables in $f$ which become fictive when identifying any two distinct essential variables in $f$. In the present paper we study the properties of the symmetric function with non-trivial arity gap ($2\leq gap(f)$). We prove several results concerning decomposition of the symmetric functions with non-trivial arity gap with its minors or subfunctions. We show that all non-empty sets of essential variables in symmetric functions with non-trivial arity gap are separable.
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