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In this paper, we address a question posed by L. Shapiro regarding algebraic and/or combinatorial characterizations of the elements of order 2 in the Riordan group. We present two classes of combinatorial matrices having pseudo-order 2. In one class, we find generalizations of Pascal's triangle and use some special cases to discover and prove interesting… (More)

In 2009, Shapiro posed the following question: " What is the asymptotic proportion of Dyck paths having an even number of hills? " In this paper, we answer Shapiro's question, as well as a generalization of the question to ternary paths. We find that the probability that a randomly chosen ternary path has an even number of hills approaches 125/169 as the… (More)

Determinants of matrices involving the Catalan sequence have appeared throughout the literature. In this paper, we focus on the evaluation of Hankel determinants featuring Catalan numbers by counting nonintersecting path systems in an associated Catalan digraph. We apply this approach in order to revisit and extend a result due to… (More)

- Arthur T. Benjamin, Naiomi T. Cameron
- The American Mathematical Monthly
- 2005

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)

- Naiomi T. Cameron, Kendra Killpatrick
- Discrete Mathematics
- 2009

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)

- Naiomi T. Cameron, Lynnell S. Matthews
- Ars Comb.
- 2014

- Naiomi T. Cameron, Kendra Killpatrick
- Electr. J. Comb.
- 2006

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)

- Naiomi T. Cameron, Kendra Killpatrick
- Electr. J. Comb.
- 2017

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)

- Arthur T. Benjamin, Harvey Mudd College, Naiomi T. Cameron, Jennifer J. Quinn
- 2016

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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