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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):
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