The Arity Gap of Polynomial Functions over Bounded Distributive Lattices

Miguel Couceiro, Erkko Lehtonen
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引用次数: 10

Abstract

Let $A$ and $B$ be arbitrary sets with at least two elements. The arity gap of a function $f\colon A^n\to B$ is the minimum decrease in its essential arity when essential arguments of $f$ are identified. In this paper we study the arity gap of polynomial functions over bounded distributive lattices and present a complete classification of such functions in terms of their arity gap. To this extent, we present a characterization of the essential arguments of polynomial functions, which we then use to show that almost all lattice polynomial functions have arity gap 1, with the exception of truncated median functions, whose arity gap is 2.
有界分配格上多项式函数的性差
设$A$和$B$是至少有两个元素的任意集合。函数$f\: a ^n\到B$的密度差是当$f$的基本参数被确定时其基本密度的最小减少。本文研究了有界分布格上多项式函数的度差问题,并根据函数的度差给出了这类函数的完全分类。在这种程度上,我们提出了多项式函数的基本参数的表征,然后我们用它来证明几乎所有的格多项式函数都有一个密度间隙1,除了截断的中位数函数,它的密度间隙为2。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
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