The size of Bruhat intervals between nested involutions in $S_{n}$
 
 
Description:  We build a chain $$\operatorname{id}=\vartheta_{0} < \vartheta_{1} < \cdots < \vartheta_{\fl{\frac{n}{2}}-1} < \vartheta_{\fl{\frac{n}{2}}}$$ of nested involutions in the Bruhat ordering of $S_{n}$, with $\vartheta_{\fl{\frac{n}{2}}}$ the maximal element for the Bruhat order, and we study the cardinality of the Bruhat intervals $\[\vartheta_{j},\vartheta_{k}\]$ for all $0 \leq j < k \leq \fl{\frac{n}{2}}$, and the number of permutations incomparable with $\vartheta_{t}$, for all $0 \leq t \leq \fl{\frac{n}{2}}$.
Area(s):
Date:  2006-09-26
Start Time:   14:45
Speaker:  Alessandro Conflitti (CMUC)
Place:  5.5
Research Groups: -Algebra and Combinatorics
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