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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)

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)

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 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)

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