论文标题
Bruhat顺序的自偶间隔
Self-dual intervals in the Bruhat order
论文作者
论文摘要
Björner-ekedahl证明了Bruhat订单的一般间隔$ [e，w] $是“最高的”，至少在$ i $ th Corank中的元素与$ i $ -th的排名一样多。 Carrell和Lakshmibai-Sandhya的众所周知的结果给出了平等的情况：$ [e，w] $在且仅当排列$ w $避免使用$ 3412 $和$ 4231 $的情况下，这些$ W $正是这些$ W $，这些$ W $是Schubert Variety $ x_w $ x_w $ smoothe flooks flues。 在本文中，我们研究了等级间隔$ [e，w] $的更精细的结构，超出其等级功能。特别是，我们表明，如果一个人算出不同等级之间的关系，这些间隔仍然是“最重的”。当$ [e，w] $作为poset自式伪装时，在这种情况下的平等案例发生；我们通过图案避免和其他几种方式来表征这些$ w $。
Björner-Ekedahl prove that general intervals $[e,w]$ in Bruhat order are "top-heavy", with at least as many elements in the $i$-th corank as the $i$-th rank. Well-known results of Carrell and of Lakshmibai-Sandhya give the equality case: $[e,w]$ is rank-symmetric if and only if the permutation $w$ avoids the patterns $3412$ and $4231$ and these are exactly those $w$ such that the Schubert variety $X_w$ is smooth. In this paper we study the finer structure of rank-symmetric intervals $[e,w]$, beyond their rank functions. In particular, we show that these intervals are still "top-heavy" if one counts cover relations between different ranks. The equality case in this setting occurs when $[e,w]$ is self-dual as a poset; we characterize these $w$ by pattern avoidance and in several other ways.
