论文标题
关于置换差距约束的置换模式
On permutation patterns with constrained gap sizes
论文作者
论文摘要
我们考虑避免在连续字母对之间具有指定差距大小的置换模式。我们称之为具有这种约束遥远模式（DPS）的模式，并显示了它们与过去研究的其他模式概念的关系。获得了2个字母的DPS的新结果。此外，我们展示了如何使用DPS证明没有计算机的两个以前的Kuszmaul猜想。此外，我们通过查看具有紧密间隙约束的一类DPS来推断出一组排列之间的惊人关系，避免了经典模式$ 123 $和$ 132 $。还讨论了Stanley-Wilf的一些有趣的DPS猜想。
We consider avoidance of permutation patterns with designated gap sizes between pairs of consecutive letters. We call the patterns having such constraints distant patterns (DPs) and we show their relation to other pattern notions investigated in the past. New results on DPs with 2 and 3 letters are obtained. Furthermore, we show how one can use DPs to prove two former conjectures of Kuszmaul without a computer. In addition, we deduce a surprising relation between the sets of permutations avoiding the classical patterns $123$ and $132$ by looking at a class of DPs with tight gap constraints. Some interesting analogues of the Stanley-Wilf former conjecture for DPs are also discussed.
