Bender-Knuth transformation from a perspective of hives

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  • Bender-Knuth transformation from a perspective of hives (Computer Algebra --Theory and its Applications)

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Kostka numbers Kλμ are non-negative integers indexed by two partitions λ and μ.They equal to the number of semistandard tableaux of shape入andweightμ. Also they equal to the number of K-hives with boundary edge label determined by λ and μ.Their basic property is Kλμ=Kλσ(μ) for any element a of the symmetric group. This is proved by constructing a bijection called the Bender-Knuth transformation between semistandard tableaux. In this paper, we give a perspective of the Bender-Knuth transformation through the hive model.

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