链上多项式函数的表示与刻画
Representations and characterizations of polynomial functions on chains
摘要：
我们感兴趣的是格多项式函数f：L^n -> L的表示和刻画，其中L是给定的有界分配格.在配套文件[arXiv 0901.4888，arXiv 0808.2619]，我们研究了某些表示，并提供了这些功能的各种特征，无论是作为某些函数方程的解决方案，并在充要条件。在本文中，我们研究这些表示和特征的特殊情况下，当L是一个链，即，一个完全有序的晶格更确切地说，我们讨论了表示格多项式函数的标准单纯形，我们提出了新的公理化这些功能放宽一些条件[arXiv 0901.4888，arXiv 0808.2619]，并考虑进一步的条件，即共单调性和极大性。
英文摘要：
We are interested in representations and characterizations of lattice polynomial functions f:L^n -> L, where L is a given bounded distributive lattice. In companion papers [arXiv 0901.4888, arXiv 0808.2619], we investigated certain representations and provided various characterizations of these functions both as solutions of certain functional equations and in terms of necessary and sufficient conditions. In the present paper, we investigate these representations and characterizations in the special case when L is a chain, i.e., a totally ordered lattice. More precisely, we discuss representations of lattice polynomial functions given in terms of standard simplices and we present new axiomatizations of these functions by relaxing some of the conditions given in [arXiv 0901.4888, arXiv 0808.2619] and by considering further conditions, namely comonotonic minitivity and maxitivity.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
