Looking at Numbers

• Main Authors: Johnson, Tom (Author), Jedrzejewski, Franck (Author)
• Corporate Author: SpringerLink (Online service)
• Format: Electronic eBook
• Language: English
• Published: Basel : Springer Basel : Imprint: Birkhäuser, 2014.
• Subjects: Mathematics.; Graph theory.; Graph Theory.; Mathematics, general.; Mathematics in Music.

Galileo Galilei said he was “reading the book of nature” as he observed pendulums swinging, but he might also simply have tried to draw the numbers themselves as they fall into networks of permutations or form loops that synchronize at different speeds, or attach themselves to balls passing in and o...

Table of Contents:

• Introduction
• 1. Permutations
• 1.1 Symmetric Group
• 1.2 Bruhat Order
• 1.3 Euler Characteristic
• 1.4 Group Action
• 1.5 Permutohedra and Cayley Graphs
• 1.6 Coxeter Groups
• 1.7 Homometric Sets
• 2. Sums
• 2.1 Integer Partitions
• References
• 3. Subsets
• 3.1 Combinatorial Designs
• 4 Kirkman’s Ladies, a Combinatorial Design
• 4.1 Steiner and Kirkman Systems
• 5. Twelve
• 5.1 (12,4,3)
• 6. (9,4,3)
• 6.1 Decomposition of Block Designs
• 7. 55 Chords
• 7.1 Chords and Designs.-8. Clarinet Trio
• 8.1 Strange Fractal Sequences
• 9. Loops
• 9.1 Self-Replicating Melodies
• 9.2 Rhythmic Canons.-10. Juggling
• 10.1 Juggling, Groups, and Braids
• 11. Unclassified
• 11.1 Some Other Designs
• A Figures
• References.