The forgotten monoid

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dc.creatorNovelli, Jean-Christophe
dc.creatorSchilling, Anne
dc.date2007-06-20
dc.date2007-10-24
dc.date.accessioned2026-07-07T09:45:08Z
dc.date.available2026-07-07T09:45:08Z
dc.descriptionWe study properties of the forgotten monoid which appeared in work of Lascoux and Schutzenberger 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^2-3n+4 forgotten classes in the symmetric group S_n. 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.
dc.description13 pages; in version 3 the proof of Proposition 3 is corrected
dc.identifierhttps://arxiv.org/abs/0706.2996
dc.identifierhttp://arxiv.org/abs/0706.2996
dc.identifierRIMS Kokyuroku Bessatsu B8 (2008) 71-83
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/163103
dc.subjectCombinatorics
dc.titleThe forgotten monoid
dc.typetext

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