排列中的笼状子序列

中文摘要 AI 辅助

给定实数序列𝔞:=(a₁,…,aₙ)，若子序列𝔟=(a_{i₁},…,a_{i_k})的最大和最小元素分别为a_{i₁}和a_{i_k}（顺序不一定对应），则称𝔟为“笼状”。本文研究n元对称群Sₙ中排列的最大笼状序列问题，还针对随机排列研究该问题，包括从所有排列中均匀选取，以及通过RSK对应从矩形排列中均匀选取的情况。

英文摘要

Given a sequence $\mathfrak{a}:=(a_1,\ldots,a_n)$ of reals, a subsequence $\mathfrak{b}=(a_{i_1},\ldots,a_{i_k})$ is said to be "caged" if the largest and smallest among the members of $\mathfrak{b}$ are $a_{i_1}$ and $a_{i_k}$, though not necessarily in that order. In this paper, we consider the problem of maximal caged sequences in permutations $π\in S_n$. We also consider the same problem for a random permutation, both when the permutation is chosen uniformly at random and also when it is picked uniformly at random from among the permutations of rectangular shape, via the RSK correspondence.

发表机构

• Indian Institute of Science（印度科学研究所）
• Indian Institute of Technology Bombay（孟买印度理工学院）

机构由 AI 辅助整理，请以论文原文为准。