The Forgotten Monoid
نویسنده
چکیده
We study properties of the forgotten monoid which appeared in work of Lascoux and Schützenberger and recently resurfaced in the construction of dual equivalence graphs by Assaf. In particular, we provide an explicit characterization of the forgotten classes in terms of inversion numbers and show that there are n − 3n + 4 forgotten classes in the symmetric group Sn. Each forgotten class contains a canonical element that can be characterized by pattern avoidance. We also show that the sum of Gessel’s quasi-symmetric functions over a forgotten class is a 0-1 sum of ribbon-Schur functions proving a conjecture by Assaf.
منابع مشابه
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