Abstract
We determine the largest difference between the number of atoms and number of coatoms of a Bruhat interval of the symmetric group $S_n$. We then pose the question of describing such extremal intervals $[u,v] \subset S_n$ and give a partial description by specifying the elements $v$ that can occur.
Highlights
We determine the largest difference between the number of atoms and number of coatoms of a Bruhat interval of the symmetric group Sn
Much work has been done on understanding the structure of Bruhat intervals of the symmetric group
Particular interest has arisen in understanding the number of atoms and coatoms of Bruhat intervals of the symmetric group [AR06, Kob11]
Summary
Much work has been done on understanding the structure of Bruhat intervals of the symmetric group (see, e.g., [BW82], [Hul03] and [BB05] along with references therein). Particular interest has arisen in understanding the number of atoms and coatoms of Bruhat intervals of the symmetric group [AR06, Kob11]. There, the maximum number of atoms and coatoms of an interval of a given length is determined.
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