2007/09/06 by Naiomi T. Cameron, Cameron, Naiomi, Kendra Killpatrick +1
Computer Science · Mathematics · Physics and Astronomy · #05A17 #05E10 #Advanced Combinatorial Mathematics #Advanced Mathematical Theories and Applications #Algorithms and Data Compression #Combinatorics (math.CO) #FOS: Mathematics
paper · pdf · doi:10.48550/arxiv.0709.0971
openalex publication_date 2007/09/06 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.