可洗牌兼容的排列统计量 II：外峰集
组合数学
2022-01-20 v3
摘要
本文是Gessel与Zhuang的arXiv:1706.00750的续作（但可独立于后者阅读）。我们研究排列统计量的洗牌兼容性——该概念由arXiv:1706.00750引入，尽管其诸多实例此前已散见于文献中。我们证明（正如Gessel与Zhuang所猜想的）外峰集统计量（Epk）是洗牌兼容的。此外，我们引入“LR-洗牌兼容”统计量的概念，其强于洗牌兼容性。我们证明Epk及另外几个统计量是LR-洗牌兼容的。进一步地，我们将这些概念与拟对称函数相联系，特别是其与上的树形结构。
引用
@article{arxiv.1806.04114,
title = {Shuffle-compatible permutation statistics II: the exterior peak set},
author = {Darij Grinberg},
journal= {arXiv preprint arXiv:1806.04114},
year = {2022}
}
备注
66 pages; a more detailed version is archived as an ancillary file. v3 has been updated, particularly with a new Question 2.51, as well as Remark 2.41 and Example 2.43, as well as fewer errors thanks to a helpful referee