论文标题
可行区域，用于连续避免模式排列的模式
The feasible regions for consecutive patterns of pattern-avoiding permutations
论文作者
论文摘要
我们研究了可行区域，以进行连续的避免模式排列的模式。更确切地说，考虑到避免固定模式的家庭$ \ Mathcal c $ co $，我们考虑了$ \ Mathcal c $的大型排列上连续模式的比例限制。这些限制形成了一个区域，我们称之为连续模式可行的区域，以$ \ Mathcal c $。 我们确定所有家庭的连续模式可行区域的尺寸$ \ MATHCAL C $以直接和偏斜的总和关闭。这些家庭包括避免单一模式和所有替代封闭类的家庭。我们进一步表明，这些区域始终是凸，我们猜想它们始终是多面体。当$ \ Mathcal c $是$τ$ - 避免$τ$的置换时，我们证明了这一猜想，其中$τ$的$τ$是单调图案的三个或$τ$。此外，在这些情况下，我们通过循环多面体给出了这些多面体的顶点的完整描述。 在此过程中，我们讨论了这项工作的联系，并与避免模式排列的包装模式的问题以及研究避免模式排列的局部限制的研究。
We study the feasible region for consecutive patterns of pattern-avoiding permutations. More precisely, given a family $\mathcal C$ of permutations avoiding a fixed set of patterns, we consider the limit of proportions of consecutive patterns on large permutations of $\mathcal C$. These limits form a region, which we call the consecutive patterns feasible region for $\mathcal C$. We determine the dimension of the consecutive patterns feasible region for all families $\mathcal C$ closed either for the direct sum or the skew sum. These families include for instance the ones avoiding a single pattern and all substitution-closed classes. We further show that these regions are always convex and we conjecture that they are always polytopes. We prove this conjecture when $\mathcal C$ is the family of $τ$-avoiding permutations, with either $τ$ of size three or $τ$ a monotone pattern. Furthermore, in these cases we give a full description of the vertices of these polytopes via cycle polytopes. Along the way, we discuss connections of this work with the problem of packing patterns in pattern-avoiding permutations and to the study of local limits for pattern-avoiding permutations.
