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The forgotten monoid

Abstract : 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 n2-3n+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.
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https://hal-upec-upem.archives-ouvertes.fr/hal-00622796
Contributor : Jean-Christophe Novelli <>
Submitted on : Monday, September 12, 2011 - 4:38:23 PM
Last modification on : Wednesday, February 26, 2020 - 7:06:05 PM

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  • HAL Id : hal-00622796, version 1

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Jean-Christophe Novelli, Anne Schilling. The forgotten monoid. RIMS Kokyuroku Bessatsu, 2008, B8 (-), pp.71-83. ⟨hal-00622796⟩

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