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- Member of: ASU Electronic Theses and Dissertations
Description
A central concept of combinatorics is partitioning structures with given constraints. Partitions of on-line posets and on-line graphs, which are dynamic versions of the more familiar static structures posets and graphs, are examined. In the on-line setting, vertices are continually added to a poset or graph while a chain partition or coloring (respectively) is maintained. %The optima of the static cases cannot be achieved in the on-line setting. Both upper and lower bounds for the optimum of the number of chains needed to partition a width $w$ on-line poset exist. Kierstead's upper bound of $\frac{5^w-1}{4}$ was improved to $w^{14 \lg w}$ by Bosek and Krawczyk. This is improved to $w^{3+6.5 \lg w}$ by employing the First-Fit algorithm on a family of restricted posets (expanding on the work of Bosek and Krawczyk) . Namely, the family of ladder-free posets where the $m$-ladder is the transitive closure of the union of two incomparable chains $x_1\le\dots\le x_m$, $y_1\le\dots\le y_m$ and the set of comparabilities $\{x_1\le y_1,\dots, x_m\le y_m\}$. No upper bound on the number of colors needed to color a general on-line graph exists. To lay this fact plain, the performance of on-line coloring of trees is shown to be particularly problematic. There are trees that require $n$ colors to color on-line for any positive integer $n$. Furthermore, there are trees that usually require many colors to color on-line even if they are presented without any particular strategy. For restricted families of graphs, upper and lower bounds for the optimum number of colors needed to maintain an on-line coloring exist. In particular, circular arc graphs can be colored on-line using less than 8 times the optimum number from the static case. This follows from the work of Pemmaraju, Raman, and Varadarajan in on-line coloring of interval graphs.
ContributorsSmith, Matthew Earl (Author) / Kierstead, Henry A (Thesis advisor) / Colbourn, Charles (Committee member) / Czygrinow, Andrzej (Committee member) / Fishel, Susanna (Committee member) / Hurlbert, Glenn (Committee member) / Arizona State University (Publisher)
Created2012
Description
Despite the wealth of folk music traditions in Portugal and the importance of the clarinet in the music of bandas filarmonicas, it is uncommon to find works featuring the clarinet using Portuguese folk music elements. In the interest of expanding this type of repertoire, three new works were commissioned from three different composers. The resulting works are Seres Imaginarios 3 by Luis Cardoso; Delirio Barroco by Tiago Derrica; and Memória by Pedro Faria Gomes. In an effort to submit these new works for inclusion into mainstream performance literature, the author has recorded these works on compact disc. This document includes interview transcripts with each composer, providing first-person discussion of each composition, as well as detailed biographical information on each composer. To provide context, the author has included a brief discussion on Portuguese folk music, and in particular, the role that the clarinet plays in Portuguese folk music culture.
ContributorsFerreira, Wesley (Contributor) / Spring, Robert S (Thesis advisor) / Bailey, Wayne (Committee member) / Gardner, Joshua (Committee member) / Hill, Gary (Committee member) / Schuring, Martin (Committee member) / Solis, Theodore (Committee member) / Arizona State University (Publisher)
Created2013
Description
This project includes a recording and performance guide for three newly commissioned pieces for the clarinet. The first piece, shimmer, was written by Grant Jahn and is for B-flat clarinet and electronics. The second piece, Paragon, is for B-flat clarinet and piano and was composed by Dr. Theresa Martin. The third and final piece, Duality in the Eye of a Bovine, was written by Kurt Mehlenbacher and is for B-flat clarinet, bass clarinet, and piano. In addition to the performance guide, this document also includes background information and program notes for the compositions, as well as composer biographical information, a list of other works featuring the clarinet by each composer, and transcripts of composer and performer interviews. This document is accompanied by a recording of the three pieces.
ContributorsPoupard, Caitlin Marie (Author) / Spring, Robert (Thesis advisor) / Gardner, Joshua (Thesis advisor) / Hill, Gary (Committee member) / Oldani, Robert (Committee member) / Schuring, Martin (Committee member) / Arizona State University (Publisher)
Created2016
Description
The primary objective of this research project is to expand the clarinet repertoire with the addition of four new pieces. Each of these new pieces use contemporary clarinet techniques, including electronics, prerecorded sounds, multiphonics, circular breathing, multiple articulation, demi-clarinet, and the clari-flute. The repertoire composed includes Grant Jahn’s Duo for Two Clarinets, Reggie Berg’s Funkalicious for Clarinet and Piano, Rusty Banks’ Star Juice for Clarinet and Fixed Media, and Chris Malloy’s A Celestial Breath for Clarinet and Electronics. In addition to the musical commissions, this project also includes interviews with the composers indicating how they wrote these works and what their influences were, along with any information pertinent to the performer, professional recordings of each piece, as well as performance notes and suggestions.
ContributorsCase-Ruchala, Celeste Ann (Contributor) / Gardner, Joshua (Thesis advisor) / Spring, Robert (Thesis advisor) / Hill, Gary (Committee member) / Rogers, Rodney (Committee member) / Schuring, Martin (Committee member) / Arizona State University (Publisher)
Created2016