Kendra Killpatrick
Pepperdine University
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Publication
Featured researches published by Kendra Killpatrick.
Journal of Combinatorial Theory | 2005
Kendra Killpatrick
Tableaux have long been used to study combinatorial properties of permutations and multiset permutations. Discovered independently by Robinson and Schensted and generalized by Knuth, the Robinson-Schensted correspondence has provided a fundamental tool for relating permutations to tableaux. In 1963, Schutzenberger defined a process called evacuation on standard tableaux which gives a relationship between the pairs of tableaux (P,Q) resulting from the Schensted correspondence for a permutation and both the reverse and the complement of that permutation. Viennot gave a geometric construction for the Schensted correspondence and Fomin described a generalization of the correspondence whicb provides a bijection between permutations and pairs of chains in Youngs lattice.In 1975, Stanley defined a Fibonacci lattice and in 1988 he introduced the idea of a differential poset. Roby gave an insertion algorithm, analogous to the Schensted correspondence, for mapping a permutation to a pair of Fibonacci tableaux. The main results of this paper are to give an evacuation algorithm for the Fibonacci tableaux that is analogous to the evacuation algorithm on Young tableaux and to describe a geometric construction for the Fibonacci tableaux that is similar to Viennots geometric construction for Young tableaux.
European Journal of Combinatorics | 2009
Kendra Killpatrick
Permutation statistics and their connections to Young tableaux have played an important role in enumerative combinatorics. Fibonacci tableaux were defined in 1975 by Stanley, but very few statistics have been defined for these tableaux. In this paper we give definitions for several statistics on Fibonacci tableaux and make connections between these statistics and known statistics for permutations. These connections allow for equidistribution results to be given on the set of standard Fibonacci tableaux.
College Mathematics Journal | 2006
Kevin Iga; Kendra Killpatrick
Kendra Killpatrick (Kendra.Killpatrick@pepperdine.edu) received her Ph.D. from the University of Minnesota in 1998 in combinatorics. She spent three years after graduation as a post-doctoral student at Colorado State University and then began teaching at Pepperdine in 2002. Her main areas of research are enumerative combinatorics, especially permutation statistics and certain differential posets called Fibonacci posets. Outside mathematics, she loves to run marathons!
Discrete Mathematics | 2009
Naiomi T. Cameron; Kendra Killpatrick
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 White for ribbon tableaux. We describe a geometric interpretation of k-ribbon Fibonacci tableaux and use this interpretation to describe a notion of P equivalence for k-ribbon Fibonacci tableaux. In addition, 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 Fomins growth diagrams.
Electronic Journal of Combinatorics | 2003
Eric S. Egge; James Haglund; Kendra Killpatrick; Darla Kremer
Electronic Journal of Combinatorics | 2012
Kendra Killpatrick
Electronic Journal of Combinatorics | 2001
Jason Bandlow; Kendra Killpatrick
Advances in Applied Mathematics | 2015
Naiomi T. Cameron; Kendra Killpatrick
Electronic Journal of Combinatorics | 2006
Naiomi T. Cameron; Kendra Killpatrick
Annals of Combinatorics | 2013
Naiomi T. Cameron; Kendra Killpatrick