ar X iv : 0 70 9 . 09 71 v 1 [ m at h . C O ] 6 S ep 2 00 7 k - RIBBON FIBONACCI TABLEAUX
نویسنده
چکیده
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 colorto-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.
منابع مشابه
ar X iv : 0 80 5 . 09 92 v 1 [ m at h . C O ] 7 M ay 2 00 8 FIBONACCI IDENTITIES AND GRAPH COLORINGS
We generalize both the Fibonacci and Lucas numbers to the context of graph colorings, and prove some identities involving these numbers. As a corollary we obtain new proofs of some known identities involving Fibonacci numbers such as Fr+s+t = Fr+1Fs+1Ft+1 + FrFsFt − Fr−1Fs−1Ft−1.
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In this paper, we give a new formulation of invariant theory for elliptic Weyl group using the group O(2, n). As an elliptic Weyl group quotient, we define a suitable C∗-bundle. We show that it has a conformal Frobenius structure which we define in this paper. Then its good section could be identified with a Frobenius manifold which we constructed in [13].
متن کاملar X iv : 0 80 5 . 09 92 v 2 [ m at h . C O ] 8 J ul 2 00 8 FIBONACCI IDENTITIES AND GRAPH COLORINGS
We generalize both the Fibonacci and Lucas numbers to the context of graph colorings, and prove some identities involving these numbers. As a corollary we obtain new proofs of some known identities involving Fibonacci numbers such as Fr+s+t = Fr+1Fs+1Ft+1 + FrFsFt − Fr−1Fs−1Ft−1.
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