tailieunhanh - Báo cáo toán học: "Domino Fibonacci Tableaux"

Tuyển tập các báo cáo nghiên cứu khoa học về toán học trên tạp chí toán học quốc tế đề tài: Domino Fibonacci Tableaux. | Domino Fibonacci Tableaux Naiomi Cameron Department of Mathematical Sciences Lewis and Clark College ncameron@ Kendra Killpatrick Department of Mathematics Pepperdine University Submitted Sep 20 2005 Accepted Apr 28 2006 Published May 5 2006 Mathematics Subject Classification 05E10 06A07 Abstract In 2001 Shimozono and White gave a description of the domino Schensted algorithm of Barbasch Vogan Garfinkle and van Leeuwen with the color-to-spin property that is the property that the total color of the permutation equals the sum of the spins of the domino tableaux. In this paper we describe the poset of domino Fibonacci shapes an isomorphic equivalent to Stanley s Fibonacci lattice Z 2 and define domino Fibonacci tableaux. We give an insertion algorithm which takes colored permutations to pairs of tableaux P Q of domino Fibonacci shape. We then define a notion of spin for domino Fibonacci tableaux for which the insertion algorithm preserves the color-to-spin property. In addition we give an evacuation algorithm for standard domino Fibonacci tableaux which relates the pairs of tableaux obtained from the domino insertion algorithm to the pairs of tableaux obtained from Fomin s growth diagrams. 1 Introduction The Fibonacci lattice Z r was introduced by Stanley in 1975 10 and like Young s lattice Yr it is one of the prime examples of an r-differential poset. In 1988 Stanley showed that for any r-differential poset P X e A 2 rn 1 XePn where A is a partition of n and e A is the number of chains in P from 0 to A. Corollary 10 In the case of Young s lattice with r 1 the Schensted insertion algorithm provides a bijective proof of this identity by taking a permutation w G Sn to a pair of standard Young tableaux P Q of the same shape A. Given w G Sn Fomin s growth diagram 2 provides another method for obtaining the same pair of standard Young tableaux provided by the Schensted insertion algorithm. THE ELECTRONIC JOURNAL OF .