Signed enumeration of ribbon tableaux: an approach through growth diagrams
نویسندگان
چکیده
We give an extension of the famous Schensted correspondence to the case of ribbon tableaux, where ribbons are allowed to be of different sizes. This is done by extending Fomin’s growth diagram approach of the classical correspondence, in particular by allowing signs in the enumeration. As an application, we give in particular a combinatorial proof, based on the Murnaghan–Nakayama rule, for the evaluation of the column sums of the character table of the symmetric group.
منابع مشابه
Signed Enumeration of Ribbon Tableaux with Local Rules and Generalizations of the Schensted Correspondence
Sergey Fomin defined the general framework of dual graded graphs that extends the classical Schensted correspondence to a much wider class of objects. His approach is both bijective and algebraic, the latter being inspired by the works of Stanley on differential posets. In this work we present an extension of Fomin’s work, through the signed enumeration of ribbon tableaux. We consider ribbons o...
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