悬崖运算符：一个层次的运算符的话
Cliff operads: a hierarchy of operads on words
摘要：
在整数字的$δ$ -cliff的线性跨度上引入了一种新的运算族.这些操作数旨在是置换操作数的类似物，也称为关联对称操作数。我们得到的操作，其部分组成可以描述的间隔的$δ$ -悬崖的晶格。这些运算在组合运算的世界中是非常特殊的，因为尽管它们的构造相对简单，但它们是无限生成的，并且它们具有非二次和非齐次的非平凡关系。我们提供了一个一般的建设，为他们的一些替代品。我们用它来赋予空间的置换，$m$ -增加树，$c$ -矩形道路，和$m$ -Dyck道路与操作结构。在$c$ -矩形路径上的运算符，如Koszul图所示，允许推广二重运算符和三重运算符的运算符。
英文摘要：
A new hierarchy of operads over the linear spans of $δ$-cliffs, which are some words of integers, is introduced. These operads are intended to be analogues of the operad of permutations, also known as the associative symmetric operad. We obtain operads whose partial compositions can be described in terms of intervals of the lattice of $δ$-cliffs. These operads are very peculiar in the world of the combinatorial operads since, despite to the relative simplicity for their construction, they are infinitely generated and they have nonquadratic and nonhomogeneous nontrivial relations. We provide a general construction for some of their quotients. We use it to endow the spaces of permutations, $m$-increasing trees, $c$-rectangular paths, and $m$-Dyck paths with operad structures. The operads on $c$-rectangular paths admit, as Koszul duals, operads generalizing the duplicial and triplicial operads.
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。
