论文标题
312避免有效的钩构和鸭单词减少
312-Avoiding Reduced Valid Hook Configurations and Duck Words
论文作者
论文摘要
有效的钩构型是用于了解West的堆栈排序图以及非交通概率理论中的累积物的组合对象。我们在312个避免置换置换术上显示了有效的钩构型，并证明了Sankar的猜想。我们扩展到所有312个避开有效的钩构型和带有指定修改的3D-DYCK单词之间的两者。我们展示了如何用3K的3D单词的数量来计数这些，其中i y的数量完全没有X，即（K，i）duck单词，并使用这种关系来证明涉及312个避免有效挂钩配置的312个属性，包括Sankar的两个猜想。我们还表明（k，1）duck单词的数量由网球数的变体给出。
Valid hook configurations are combinatorial objects used to understand West's stack sorting map as well as cumulants in noncommutative probability theory. We show a bijection between reduced valid hook configurations on 312-avoiding permutations with the maximal allowed number of points and 3D-Dyck words, proving a conjecture of Sankar's. We extend to a bijection between all 312-avoiding reduced valid hook configurations and 3D-Dyck words with specified modifications. We show how these can be counted in terms of the number of 3D-Dyck words of length 3k in which exactly i Y's do not have an X immediately before them, the (k,i)-Duck words, and use this relationship to prove several properties about sums of 312-avoiding reduced valid hook configurations, including two more of Sankar's conjectures. We also show that the number of (k,1)-Duck words is given by a variant of the tennis ball numbers.
