$k$-Ribbon Fibonacci Tableaux

Details $k$-Ribbon Fibonacci Tableaux $k$-Ribbon Fibonacci Tableaux

2007-09-06

arxiv.org/abs/0709.0971v1

Mathematics

Combinatorics

33 pages

Scientific paper

We extend the notion of $k$-ribbon tableaux to the Fibonacci lattice, a differential poset defined by R. Stanley in 1975. Using this notion, we describe an insertion algorithm that takes $k$-colored permutations to pairs of $k$-ribbon Fibonacci tableaux of the same shape, and we demonstrate a color-to-spin property, similar to that described by Shimozono and White for ribbon tableaux. We give an evacuation algorithm which relates the pair of $k$-ribbon Fibonacci tableaux obtained through the insertion algorithm to the pair of $k$-ribbon Fibonacci tableaux obtained using Fomin's growth diagrams. In addition, we present an analogue of Knuth relations for $k$-colored permutations and $k$-ribbon Fibonacci tableaux.

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