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An application of maximum-minimum distance circuits on hypercubes

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Combinatorial Mathematics

Part of the book series: Lecture Notes in Mathematics ((LNM,volume 686))

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Abstract

The related questions of finding Hamilton circuits in the n-dimensional cube with d points on an edge which maximize the minimum "taxicab" distance between successive vertices and/or which maximize the sum of such distances over the entire circuit is investigated. A "good" bound for the first quantity and an achievable limit for the second are developed and several optimal constructions found. Both of these circuits are central to designing pseudo-color graphics displays in which minimal grey scale differences become maximal color differences.

This work was supported by the U. S. Energy Research and Development Administration (ERDA) under Contract No. AT(29-1)-789.

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Bibliography

  1. E. N. Gilbert, "Gray Codes and Paths on the n-Cube," Bell System Tech. Jour. (37) 3 (1958), 815–825.

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  5. W. D. Wright, "The Graphical Representation of Small Color Differences," Jour. of the Optical Soc. of Amer. (33) 11 (1943), 632–636.

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Authors and Affiliations

  1. Department of Applied Mathematics, Sandia Laboratories, 87115, Albuquerque, New Mexico, USA

    Gustavus J. Simmons

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  1. Gustavus J. Simmons
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D. A. Holton Jennifer Seberry

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© 1978 Springer-Verlag

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Simmons, G.J. (1978). An application of maximum-minimum distance circuits on hypercubes. In: Holton, D.A., Seberry, J. (eds) Combinatorial Mathematics. Lecture Notes in Mathematics, vol 686. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0062544

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  • DOI: https://doi.org/10.1007/BFb0062544

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-08953-7

  • Online ISBN: 978-3-540-35702-5

  • eBook Packages: Springer Book Archive

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