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Medientyp:
E-Artikel
Titel:
Canonical Decompositions of Affine Permutations, Affine Codes, and Split $k$-Schur Functions
Beteiligte:
Denton, Tom
Erschienen:
The Electronic Journal of Combinatorics, 2012
Erschienen in:The Electronic Journal of Combinatorics
Sprache:
Nicht zu entscheiden
DOI:
10.37236/2248
ISSN:
1077-8926
Entstehung:
Anmerkungen:
Beschreibung:
<jats:p>We develop a new perspective on the unique maximal decomposition of an arbitrary affine permutation into a product of cyclically decreasing elements, implicit in work of Thomas Lam. This decomposition is closely related to the affine code, which generalizes the $k$-bounded partition associated to Grassmannian elements. We also prove that the affine code readily encodes a number of basic combinatorial properties of an affine permutation. As an application, we prove a new special case of the Littlewood-Richardson Rule for $k$-Schur functions, using the canonical decomposition to control for which permutations appear in the expansion of the $k$-Schur function in noncommuting variables over the affine nil-Coxeter algebra.</jats:p>