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An affine generalization of evacuation

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arxiv 1806.07429 v1 pith:ACIRSZ5A submitted 2018-06-19 math.CO

M. Chmutov , G. Frieden , D. Kim , J.B. Lewis , E. Yudovina This is my paper · ORCID
classification math.CO
keywords evacuationaffineanalogouscertaindomino-likeestablishevaluatingexistence
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abstract

We establish the existence of an involution on tabloids that is analogous to Schutzenberger's evacuation map on standard Young tableaux. We find that the number of its fixed points is given by evaluating a certain Green's polynomial at $q = -1$, and satisfies a "domino-like" recurrence relation.

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  1. Two-row $W$-graphs in affine type $A$

    math.CO 2019-08 conditional novelty 7.0 of 10

    Two-row shapes in affine type A admit finite W-graphs, constructed combinatorially and proven unique up to isomorphism, extending the known finite-type picture.

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