Naiomi T. Cameron

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1. THE PROBLEM OF THE DETERMINED ANTS. Imagine four determined ants who simultaneously walk along the edges of the picnic table graph of Figure 1. The ants can move only to the right (northeast, southeast, and sometimes due east) with the goal of reaching four different morsels. d d d d d d d d d d d d d d d d d d d d d d d d d d d d d d d d d d
In this paper, we provide combinatorial interpretations for some deter-minantal identities involving Fibonacci numbers. We use the method due to Lindström-Gessel-Viennot in which we count nonintersecting n-routes in carefully chosen digraphs in order to gain insight into the nature of some well-known determinantal identities while allowing room to(More)
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(More)
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(More)
We consider the classical Mahonian statistics on the set B n (Σ) of signed permutations in the hyperoctahedral group B n which avoid all patterns in Σ, where Σ is a set of patterns of length two. In 2000, Simion gave the cardinality of B n (Σ) in the cases where Σ contains either one or two patterns of length two and showed that |B n (Σ)| is constant(More)
In this paper, we provide combinatorial interpretations for some determinantal identities involving Fibonacci numbers. We use the method due to Lindström-Gessel-Viennot in which we count nonintersecting n-routes in carefully chosen digraphs in order to gain insight into the nature of some well-known determinantal identities while allowing room to generalize(More)
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