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Permutations

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Looking at Numbers

Abstract

Despite the fact that I am a musician and composer, this is not a book about music. It is a book about “looking at numbers.” Sometimes a particular number in one of these drawings represents a particular note in a particular composition, but all the numbers here represent a particular point in some sort of logical sequence, in some system of permutations or combinations, in some network of sets and subsets.

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References

  1. Björner, A., and F. Brenti. 2005. Combinatorics of Coxeter Groups. New York: Springer.

    Google Scholar 

  2. Coxeter, H.S.M. 1959. Introduction to Geometry. New York: Wiley.

    Google Scholar 

  3. Coxeter, H.S.M. 1963. Regular Polytopes. New York: Macmillan.

    Google Scholar 

  4. Coxeter, H.S.M. 1999. The Beauty of Geometry: Twelve Essays. Mineola: Dover Publications.

    Google Scholar 

  5. Jedrzejewski, F. 2005. Permutation groups and chord tessellations. In Proceedings of the International Computer Music Conference, 231–234. Barcelona.

    Google Scholar 

  6. Mandereau, J., D. Ghisi, E. Amiot, M. Andreatta, and C. Agon. 2011. Z-relation and homometry in musical distributions. Journal of Mathematics and Music 5(2): 83–98.

    Article  MathSciNet  MATH  Google Scholar 

  7. Mandereau, J., D. Ghisi, E. Amiot, M. Andreatta, and C. Agon. 2011. Discrete phase retrieval in musical structures. Journal of Mathematics and Music 5(2): 99–116.

    Article  MathSciNet  MATH  Google Scholar 

  8. Patterson, A.L. 1944. Ambiguities in the X-ray analysis of crystal structure. Physical Review 65: 195–201.

    Article  Google Scholar 

  9. Rosenblatt, J. 1984. Phase Retrieval. Communications in Mathematical Physics 95: 317–343.

    Article  MathSciNet  MATH  Google Scholar 

  10. O’Rourke, J., P. Taslakian, and G. Toussaint. 2008. A Pumping Lemma for Homometric Rhythms, 20th Canadian Conference on Computational Geometry. Montreal.

    Google Scholar 

  11. Stein, S.K., S. Szabó. 1994. Algebra and Tiling, The Carus Mathematical Monographs. Washington, DC: Mathematical Association of America.

    Google Scholar 

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Correspondence to Tom Johnson .

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Johnson, T., Jedrzejewski, F. (2014). Permutations. In: Looking at Numbers. Birkhäuser, Basel. https://doi.org/10.1007/978-3-0348-0554-4_1

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