*GEORGE E. ANDREWS*

- Published in print:
- 2013
- Published Online:
- September 2013
- ISBN:
- 9780199656592
- eISBN:
- 9780191748059
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780199656592.003.0010
- Subject:
- Mathematics, Combinatorics / Graph Theory / Discrete Mathematics, History of Mathematics

While Leibniz appears to have been the earliest to consider the partitioning of integers into sums, Euler was the first person to make truly deep discoveries. J. J. Sylvester was the next researcher ...
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While Leibniz appears to have been the earliest to consider the partitioning of integers into sums, Euler was the first person to make truly deep discoveries. J. J. Sylvester was the next researcher to make major contributions, followed by Fabian Franklin. The 20th century saw an explosion of research with contributions from L. J. Rogers, G. H. Hardy, Percy MacMahon, Srinivasa Ramanujan, and Hans Rademacher.Less

While Leibniz appears to have been the earliest to consider the partitioning of integers into sums, Euler was the first person to make truly deep discoveries. J. J. Sylvester was the next researcher to make major contributions, followed by Fabian Franklin. The 20th century saw an explosion of research with contributions from L. J. Rogers, G. H. Hardy, Percy MacMahon, Srinivasa Ramanujan, and Hans Rademacher.

*Ethan Berkove, David Cervantes-Nava, Daniel Condon, Andrew Eickemeyer, Rachel Katz, and Michael J. Schulman*

- Published in print:
- 2017
- Published Online:
- May 2018
- ISBN:
- 9780691171920
- eISBN:
- 9781400889136
- Item type:
- chapter

- Publisher:
- Princeton University Press
- DOI:
- 10.23943/princeton/9780691171920.003.0008
- Subject:
- Mathematics, History of Mathematics

This chapter analyzes a puzzle related to a classic problem first posed by English mathematician Percy MacMahon. MacMahon Given a palette of six colors, a 6-color cube is one where each face is one ...
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This chapter analyzes a puzzle related to a classic problem first posed by English mathematician Percy MacMahon. MacMahon Given a palette of six colors, a 6-color cube is one where each face is one color and all six colors appear on some face. It is a straightforward counting argument to show that there are exactly thirty distinct 6-color cubes up to rigid isometry. MacMahon introduced this set of cubes and posed a number of questions about it. The most natural one—and the motivating problem for this chapter—was whether one could take twenty-seven cubes from the set and build a 3 × 3 × 3 cube where each face was one color. The chapter first provides background and terminology, including the coloring condition and a description of a useful partial order on cubes. It then applies these tools to solve the 2-color case, the 3-color problem, and the problem for frames of all sizes.Less

This chapter analyzes a puzzle related to a classic problem first posed by English mathematician Percy MacMahon. MacMahon Given a palette of six colors, a 6-color cube is one where each face is one color and all six colors appear on some face. It is a straightforward counting argument to show that there are exactly thirty distinct 6-color cubes up to rigid isometry. MacMahon introduced this set of cubes and posed a number of questions about it. The most natural one—and the motivating problem for this chapter—was whether one could take twenty-seven cubes from the set and build a 3 × 3 × 3 cube where each face was one color. The chapter first provides background and terminology, including the coloring condition and a description of a useful partial order on cubes. It then applies these tools to solve the 2-color case, the 3-color problem, and the problem for frames of all sizes.