论文标题
长度的双射击 - $ 5 $ $ 5 $的排列模式
A bijection for length-$5$ patterns in permutations
论文作者
论文摘要
$（31245,32145,31254,32154）$ - 避免排列和$（31425,32415,31524,32514）$之间的两次培训，构建了五个经典的设置统计数据。与Baril-Vajnovszki和Martinez的两种置换编码相结合证明了Gao和Kitaev提出的列举猜想。此外，事实证明，公共计数序列的生成函数被证明是代数。
A bijection between $(31245,32145,31254,32154)$-avoiding permutations and $(31425,32415,31524,32514)$-avoiding permutations is constructed, which preserves five classical set-valued statistics. Combining with two codings of permutations due respectively to Baril--Vajnovszki and Martinez--Savage proves an enumerative conjecture posed by Gao and Kitaev. Moreover, the generating function for the common counting sequence is proved to be algebraic.
