Algorithms of Schensted and Hillman-Grassl and Operations on Standard Bitableaux

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In this thesis, we describe Schensted's algorithm for finding the length of a longest increasing subsequence of a finite sequence. Schensted's algorithm also constructs a bijection between permutations of the first N natural numbers and standard bitableaux of size N. We also describe the Hillman-Grassl algorithm which constructs a bijection between reverse plane partitions and the solutions in natural numbers of a linear equation involving hook lengths. Pascal programs and sample output for both algorithms appear in the appendix. In addition, we describe the operations on standard bitableaux corresponding to the operations of inverting and reversing permutations. Finally, we show ... continued below

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iv, 101 leaves

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Sutherland, David C. (David Craig) August 1983.

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  • Sutherland, David C. (David Craig)

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In this thesis, we describe Schensted's algorithm for finding the length of a longest increasing subsequence of a finite sequence. Schensted's algorithm also constructs a bijection between permutations of the first N natural numbers and standard bitableaux of size N. We also describe the Hillman-Grassl algorithm which constructs a bijection between reverse plane partitions and the solutions in natural numbers of a linear equation involving hook lengths. Pascal programs and sample output for both algorithms appear in the appendix. In addition, we describe the operations on standard bitableaux corresponding to the operations of inverting and reversing permutations. Finally, we show that these operations generate the dihedral group D_4

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iv, 101 leaves

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  • August 1983

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  • May 10, 2015, 6:16 a.m.

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  • Dec. 16, 2016, 12:22 p.m.

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Sutherland, David C. (David Craig). Algorithms of Schensted and Hillman-Grassl and Operations on Standard Bitableaux, thesis, August 1983; Denton, Texas. (digital.library.unt.edu/ark:/67531/metadc503902/: accessed August 17, 2018), University of North Texas Libraries, Digital Library, digital.library.unt.edu; .