论文标题
有限的仿射排列I.模式回避和枚举
Bounded affine permutations I. Pattern avoidance and enumeration
论文作者
论文摘要
我们引入了一种新的有界条件，以实现仿射排列，这是由统计物理学中周期性边界条件的富有成果的概念所激发的。我们研究有界仿射排列中的避免模式。特别是，我们表明，如果$τ$是有限的增加振荡之一，那么每个$τ$ affining offine置换都会满足界限条件。我们还使用分析方法将其确切和渐近的枚举与基本普通排列的枚举相关联，我们还探索了可以分解为块的模式仿射排列的枚举。最后，我们对所有尺寸$ n $的所有有限仿射排列的集合进行了精确渐近枚举。伴侣论文将重点避免单调减少界仿射排列中的模式。
We introduce a new boundedness condition for affine permutations, motivated by the fruitful concept of periodic boundary conditions in statistical physics. We study pattern avoidance in bounded affine permutations. In particular, we show that if $τ$ is one of the finite increasing oscillations, then every $τ$-avoiding affine permutation satisfies the boundedness condition. We also explore the enumeration of pattern-avoiding affine permutations that can be decomposed into blocks, using analytic methods to relate their exact and asymptotic enumeration to that of the underlying ordinary permutations. Finally, we perform exact and asymptotic enumeration of the set of all bounded affine permutations of size $n$. A companion paper will focus on avoidance of monotone decreasing patterns in bounded affine permutations.
