论文标题
间隔停车功能
Interval parking functions
论文作者
论文摘要
间隔停车功能（IPF）是普通停车功能的概括，在该功能中，每辆车只能在固定的空间间隔内停车。每个间隔停车功能都可以表示为一对$（a，b）$，其中$ a $是停车功能，$ b $是双停车功能。我们说，如果有一个IPF $（a，b）$，则一对$（x，y）$是\ emph {tocrable}，因此$ x，y $分别是$ a，b $的结果，是停车功能。可及性是反身性和反对称性的，但通常不一定。我们证明，它的传递闭合，即\ emph {pseudoreach ofder order}，恰恰是对称群体$ \ sym_n $的气泡 - 选项顺序，可以用du〜cloux的意义上的正常形式表示符合限制的形式；特别是，这是长度为2美元，\ dots，n $的链条的产物。因此，它被认为是阿姆斯特朗分类顺序的特殊情况，它位于布鲁哈特（Bruhat）和（左）弱点之间。
Interval parking functions (IPFs) are a generalization of ordinary parking functions in which each car is willing to park only in a fixed interval of spaces. Each interval parking function can be expressed as a pair $(a,b)$, where $a$ is a parking function and $b$ is a dual parking function. We say that a pair of permutations $(x,y)$ is \emph{reachable} if there is an IPF $(a,b)$ such that $x,y$ are the outcomes of $a,b$, respectively, as parking functions. Reachability is reflexive and antisymmetric, but not in general transitive. We prove that its transitive closure, the \emph{pseudoreachability order}, is precisely the bubble-sort order on the symmetric group $\Sym_n$, which can be expressed in terms of the normal form of a permutation in the sense of du~Cloux; in particular, it is isomorphic to the product of chains of lengths $2,\dots,n$. It is thus seen to be a special case of Armstrong's sorting order, which lies between the Bruhat and (left) weak orders.
