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Search Results: 1 - 10 of 128 matches for " Kendra Killpatrick "
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Generalized Legendre-Stirling Numbers  [PDF]
K. C. Garrett, Kendra Killpatrick
Open Journal of Discrete Mathematics (OJDM) , 2014, DOI: 10.4236/ojdm.2014.44014
Abstract: The Legendre-Stirling numbers were discovered by Everitt, Littlejohn and Wellman in 2002 in a study of the spectral theory of powers of the classical second-order Legendre differential operator. In 2008, Andrews and Littlejohn gave a combinatorial interpretation of these numbers in terms of set partitions. In 2012, Mongelli noticed that both the Jacobi-Stirling and the Legendre-Stirling numbers are in fact specializations of certain elementary and complete symmetric functions and used this observation to give a combinatorial interpretation for the generalized Legendre-Stirling numbers. In this paper we provide a second combinatorial interpretation for the generalized Legendre-Stirling numbers which more directly generalizes the definition of Andrews and Littlejohn and give a combinatorial bijection between our interpretation and the Mongelli interpretation. We then utilize our interpretation to prove a number of new identities for the generalized Legendre-Stirling numbers.
Wilf Equivalence for the Charge Statistic
Kendra Killpatrick
Mathematics , 2012,
Abstract: Savage and Sagan have recently defined a notion of st-Wilf equivalence for any permutation statistic st and any two sets of permutations $\Pi$ and $\Pi'$. In this paper we give a thorough investigation of st-Wilf equivalence for the charge statistic on permutations and use a bijection between the charge statistic and the major index to prove a conjecture of Dokos, Dwyer, Johnson, Sagan and Selsor regarding powers of 2 and the major index.
$k$-Ribbon Fibonacci Tableaux
Naiomi Cameron,Kendra Killpatrick
Mathematics , 2007,
Abstract: 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 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.
Inversion Polynomials for Permutations Avoiding Consecutive Patterns
Naiomi Cameron,Kendra Killpatrick
Mathematics , 2014,
Abstract: In 2012, Sagan and Savage introduced the notion of $st$-Wilf equivalence for a statistic $st$ and for sets of permutations that avoid particular permutation patterns which can be extended to generalized permutation patterns. In this paper we consider $inv$-Wilf equivalence on sets of two or more consecutive permutation patterns. We say that two sets of generalized permutation patterns $\Pi$ and $\Pi'$ are $inv$-Wilf equivalent if the generating function for the inversion statistic on the permutations that simultaneously avoid all elements of $\Pi$ is equal to the generating function for the inversion statistic on the permutations that simultaneously avoid all elements of $\Pi'$. In 2013, Cameron and Killpatrick gave the inversion generating function for Fibonacci tableaux which are in one-to-one correspondence with the set of permutations that simultaneously avoid the consecutive patterns $321$ and $312.$ In this paper, we use the language of Fibonacci tableaux to study the inversion generating functions for permutations that avoid $\Pi$ where $\Pi$ is a set of five or fewer consecutive permutation patterns. In addition, we introduce the more general notion of a strip tableaux which are a useful combinatorial object for studying consecutive pattern avoidance. We go on to give the inversion generating functions for all but one of the cases where $\Pi$ is a subset of three consecutive permutation patterns and we give several results for $\Pi$ a subset of two consecutive permutation patterns.
Internationalisation and the Neoliberal University
Kendra Strauss
QJB : Querelles. Jahrbuch für Frauen- und Geschlechterforschung , 2013,
Abstract: This short intervention explores recent research on gender and the status of women in geography and draws implications for the ramifications of the internationalisation in the context of the neoliberal university. In einer kurzen Intervention werden die Ergebnisse der aktuellen Geschlechterforschung sowie die Situation von Wissenschaftlerinnen im Fach Geographie betrachtet und daraus Schlussfolgerungen für die Auswirkungen der Internationalisierung im Kontext des Konzepts der neoliberalen Universit t gezogen.
Feed Sack Fashion in Rural America: A Reflection of Culture
Kendra Brandes
Online Journal of Rural Research & Policy , 2009, DOI: 10.4148/ojrrp.v4i1.59
Abstract: The recycling of cotton feed sacks into apparel and household items was a common practice across rural America during the first half of the twentieth century. This creative recycling of a utilitarian fabric has, until recently, been omitted from histories of American fashion because the practice centered on fabric use rather than new garment styles, and because the farm wife of rural America was not considered to be a source of fashion inspiration. As an element of material culture, the clothing and clothing practices of rural populations reflect the life and times of the era to the same extent as that of the general population. However, it is the activities of these farm wives, clothing their families in feed sacks, that offer a view of life that was unique to rural communities during this time period. This project collected oral histories of individuals who shared memories of using feed sacks during the 1930s through the 1950s. The memories not only confirmed the wide spread use of feed sacks for clothing and house hold goods, but provided a glimpse of everyday life in rural America during this time period.
Review Essay: Guides to Writing about Music
Kendra Leonard
Journal of Music History Pedagogy , 2011,
Abstract: Guides to writing about music have become staples in courses on music history. This review covers three such books, by Bellman, Herbert, and Wingell, as well as RILM’s reference on musical terms and conventions. The review discusses the strengths or weaknesses of all four books in order to help an instructor decide what might be best for any particular course.
The Role of Social Capital for Black Students at Predominantly White Institutions
Kendra D. Stewart
Sociation Today , 2011,
Abstract: Past research studies have pointed to how such adverse social conditions have led to the existence of lower rates of social satisfaction and identification with campus for Black college students at predominantly White student colleges. Research shows that access to Black student associations provide social networks that a) encouraged greater interaction with staff and faculty outside of the classroom; b) validated their on-campus experiences; c) promoted strong racial/ethnic attitudes; d) allowed for more access to student support services; e) strengthened identity development and their pursuit of a social justice agenda.
Visualization of Word Usage in Fluid Mechanics Abstracts
Eric Mockensturm,Kendra Sharp
Physics , 2009,
Abstract: The fluid dynamics video linked in the document shows how `keywords' from abstracts contained in three journals--Physics of Fluids (A) from 1970, Experiments in Fluids from 1983, and Journal of Fluid Mechanics from 1954--have changed over time.
Kostka-Foulkes polynomials and Macdonald spherical functions
Kendra Nelsen,Arun Ram
Mathematics , 2004,
Abstract: Generalized Hall-Littlewood polynomials (Macdonald spherical functions) and generalized Kostka-Foulkes polynomials ($q$-weight multiplicities) arise in many places in combinatorics, representation theory, geometry, and mathematical physics. This paper attempts to organize the different definitions of these objects and prove the fundamental combinatorial results from ``scratch'', in a presentation which, hopefully, will be accessible and useful for both the nonexpert and researchers currently working in this very active field. The combinatorics of the affine Hecke algebra plays a central role. The final section of this paper can be read independently of the rest of the paper. It presents, with proof, Lascoux and Sch\"utzenberger's positive formula for the Kostka-Foulkes poynomials in the type A case.
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