Geodesic
On the complexity of computing Kostka numbers and Littlewood-Richardson coefficients
Journal of Algebraic Combinatorics, Tome 24 (2006) no. 3, pp. 347-354.

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Summary: 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 at-tention in the past, and was raised recently by E. Rassart in [11]. We prove that the problem of computing either quantity is # $P$-complete. Thus, unless $P = NP$, which is widely disbelieved, there do not exist efficient algorithms that compute these numbers.
Keywords: keywords Kostka numbers, Littlewood-Richardson coefficients, computational complexity 
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     title = {On the complexity of computing {Kostka} numbers and {Littlewood-Richardson} coefficients},
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Narayanan, Hariharan. On the complexity of computing Kostka numbers and Littlewood-Richardson coefficients. Journal of Algebraic Combinatorics, Tome 24 (2006) no. 3, pp. 347-354. http://geodesic.mathdoc.fr/item/JAC_2006__24_3_a0/