Ja n 20 05 The computation of Kostka numbers and Littlewood - Richardson coefficients is # P - complete
نویسنده
چکیده
Kostka numbers and Littlewood-Richardson coefficients play an essential role in the representation theory of the symmetric groups and the special linear groups. There has been a significant amount of interest in their computation ([1], [10], [11], [2], [3]). The issue of their computational complexity has been a question of folklore, but was asked explicitly by E. Rassart [10]. We prove that the computation of either quantity is #P-complete. The reduction to computing Kostka numbers, is from the #P-complete problem [4] of counting the number of 2× k contingency tables having given row and column sums. The main ingredient in this reduction is a correspondence discovered by D. E. Knuth [6]. The reduction to the problem of computing Littlewood-Richardson coefficients is from that of computing Kostka numbers.
منابع مشابه
On the complexity of computing Kostka numbers and Littlewood-Richardson coefficients
Kostka numbers and Littlewood-Richardson coefficients appear in combinatorics and representation theory. Interest in their computation stems from the fact that they are present in quantum mechanical computations since Wigner [15]. In recent times, there have been a number of algorithms proposed to perform this task [1–3, 11, 12]. The issue of their computational complexity has received attentio...
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