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Random Geometric Graphs

Mathew Penrose

Published in print:
2003
Published Online:
September 2007
ISBN:
9780198506263
eISBN:
9780191707858
Item type:
book
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780198506263.001.0001
Subject:
Mathematics, Probability / Statistics

This book sets out a body of rigorous mathematical theory for finite graphs with nodes placed randomly in Euclidean d-space according to a common probability density, and edges added to connect ... More


PRODUCTS AND RETRACTS

Pavol Hell and Jaroslav Nešetřil

in Graphs and Homomorphisms

Published in print:
2004
Published Online:
September 2007
ISBN:
9780198528173
eISBN:
9780191713644
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780198528173.003.0002
Subject:
Mathematics, Combinatorics / Graph Theory / Discrete Mathematics

This chapter focuses on certain basic constructions that occur frequently in the rest of the book, emphasizing the product and the retract, but also considering other constructs. These include the ... More


MAXIMUM DEGREE, CLIQUES, AND COLOURINGS

Mathew Penrose

in Random Geometric Graphs

Published in print:
2003
Published Online:
September 2007
ISBN:
9780198506263
eISBN:
9780191707858
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780198506263.003.0006
Subject:
Mathematics, Probability / Statistics

This chapter is concerned with maximum degree, clique number, and chromatic number. A focusing (i.e., two-point concentration) phenomenon is demonstrated for the distribution of the maximum degree in ... More


ORBIT COUNTING AND THE TUTTE POLYNOMIAL

Peter J. Cameron

in Combinatorics, Complexity, and Chance: A Tribute to Dominic Welsh

Published in print:
2007
Published Online:
September 2007
ISBN:
9780198571278
eISBN:
9780191718885
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780198571278.003.0001
Subject:
Mathematics, Probability / Statistics

This chapter summarizes the various attempts to extend the Tutte polynomial of a matroid to a polynomial which counts orbits of a group on various sets of objects that the usual Tutte polynomial ... More


Chromatic Tonal Spacesm

Fred Lerdahl

in Tonal Pitch Space

Published in print:
2005
Published Online:
May 2008
ISBN:
9780195178296
eISBN:
9780199870370
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780195178296.003.0006
Subject:
Music, Theory, Analysis, Composition

This chapter extends the diatonic model of Chapter 2 to chromatic spaces that are relevant to the music of the late 19th and early 20th centuries. First, the evolution of pitch space is demonstrated ... More


Duke Bluebeard's Castle: Toward Character Reversal: Reassignment of Pentatonic and Whole‐Tone Spheres

Elliott Antokoletz

in Musical Symbolism in the Operas of Debussy and Bartok

Published in print:
2008
Published Online:
May 2008
ISBN:
9780195365825
eISBN:
9780199868865
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780195365825.003.0010
Subject:
Music, Opera

This chapter looks at Doors II (Armoury), III (Treasure Chamber), and IV (Garden) and develops Judith's “Fate” motif and the leitmotif of Stefi Geyer, including the transformation between Judith's ... More


Accentuation in Practice

Clive Brown

in Classical and Romantic Performing Practice 1750-1900

Published in print:
1999
Published Online:
May 2008
ISBN:
9780198161653
eISBN:
9780191716263
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780198161653.003.0003
Subject:
Music, Ethnomusicology, World Music

This chapter investigates the relationship between theory and practice in accentuation. It deals with the ways in which notation may imply accentuation where it is not explicitly indicated, for ... More


Piano Concerto

David Manning

in Vaughan Williams on Music

Published in print:
2007
Published Online:
October 2011
ISBN:
9780195182392
eISBN:
9780199851485
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780195182392.003.0084
Subject:
Music, History, Western

The first two movements of the Piano Concerto were sketched in 1926, and the third movement in 1930. The work is dedicated to Miss Harriet Cohen. There are three movements: Toccata leading to Romanza ... More


Op. 50 (1787)

Floyd Grave and Margaret Grave

in The String Quartets of Joseph Haydn

Published in print:
2006
Published Online:
May 2008
ISBN:
9780195173574
eISBN:
9780199872152
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780195173574.003.0013
Subject:
Music, History, Western

Dedicated to Friedrich Wilhelm II and known as the “Prussian” quartets, these difficult works were clearly designed for connoisseurs. Their sale and early publication history involved complex, ... More


Op. 54/55 (1788)

Floyd Grave and Margaret Grave

in The String Quartets of Joseph Haydn

Published in print:
2006
Published Online:
May 2008
ISBN:
9780195173574
eISBN:
9780199872152
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780195173574.003.0014
Subject:
Music, History, Western

Noted for timbral brilliance and an accent on taxing first-violin delivery, this set, Op. 54/55, is traditionally linked to the violinist Johann Tost, who served as a middleman in its sale. ... More


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