The complexity of computing Kronecker coefficients

FPSAC'08 - 20th International Conference on Formal Power Series and Algebraic Combinatorics

Volumn , Issue , 2008, Pages 357-368

  Bürgisser, Peter ^a   Ikenmeyer, Christian ^a  

^a UNIVERSITY OF PADERBORN   (Germany)

Author keywords

Computational complexity; Kronecker coefficients; Representations of symmetric groups; Tensor products

Indexed keywords

COMPLEXITY CLASS; IRREDUCIBLE REPRESENTATIONS; KRONECKER COEFFICIENTS; POLYNOMIAL-TIME ALGORITHMS; SCHUR POLYNOMIALS; SYMMETRIC GROUPS; TENSOR PRODUCTS;

COMPUTATIONAL COMPLEXITY; POLYNOMIAL APPROXIMATION; TENSORS;

COMBINATORIAL MATHEMATICS;

EID: 84860440307     PISSN: None     EISSN: None     Source Type: Conference Proceeding    
DOI: None     Document Type: Conference Paper

References (22)

1. (n-p,p) * sλ. Sém. Lothar. Combin., 54A:Art. B54Af, 29 pp. (electronic), 2005/07. ISSN 1286-4889.
2. Lance Fortnow. Counting complexity. In Complexity theory retrospective, II, pages 81-107. Springer, New York, 1997.
3. William Fulton. Young tableaux, volume 35 of London Mathematical Society Student Texts. Cambridge University Press, Cambridge, 1997. ISBN 0-521-56144-2; 0-521-56724-6.
4. Adriano M. Garsia and Jeffrey Remmel. Shuffles of permutations and the Kronecker product. Graphs Combin., 1(3):217-263, 1985. ISSN 0911-0119.
5. n(C) tensor products. I. Proof of the saturation conjecture. J. Amer. Math. Soc., 12(4):1055-1090, 1999. ISSN 0894-0347.
6. Joseph M. Landsberg and Laurent Manivel. On the ideals of secant varieties of Segre varieties. Found. Comput. Math., 4(4):397-422, 2004. ISSN 1615-3375.
7. Alain Lascoux. Produit de Kronecker des représentations du groupe symétrique. In Séminaire d'Algèbre Paul Dubreil et Marie-Paule Malliavin, 32ème année (Paris, 1979), volume 795 of Lecture Notes in Math., pages 319-329. Springer, Berlin, 1980.
8. Ketan D. Mulmuley. Geometric complexity theory VI: The flip via saturated and positive integer programming in representation theory and algebraic geometry,. Technical Report TR-2007-04, Computer Science Department, The University of Chicago, 2007.
9. Ketan D. Mulmuley and Milind Sohoni. Geometric complexity theory. I. An approach to the P vs. NP and related problems. SIAM J. Comput., 31(2):496-526 (electronic), 2001. ISSN 1095-7111.
10. Ketan D. Mulmuley and Milind Sohoni. Geometric complexity theory III: On deciding positivity of Littlewood-Richardson coefficients. cs.ArXive preprint cs.CC/0501076, 2005.
11. Ketan D. Mulmuley and Milind Sohoni. Geometric complexity theory II: Towards explicit obstructions for embeddings among class varieties. cs.ArXive preprint cs.CC/0612134. To appear in SIAM J. Comput., 2006.
12. Hariharan Narayanan. On the complexity of computing Kostka numbers and Littlewood-Richardson coefficients. J. Algebraic Combin., 24(3):347-354, 2006. ISSN 0925-9899.
13. Christos H. Papadimitriou. Computational complexity. Addison-Wesley Publishing Company, Reading, MA, 1994. ISBN 0-201-53082-1.
14. Jeffrey B. Remmel. A formula for the Kronecker products of Schur functions of hook shapes. J. Algebra, 120(1):100-118, 1989. ISSN 0021-8693.
15. (1p-r;r)⊗. Discrete Math., 99(1-3):265-287, 1992. ISSN 0012-365X.
16. Jeffrey B. Remmel and Tamsen Whitehead. On the Kronecker product of Schur functions of two row shapes. Bull. Belg. Math. Soc. Simon Stevin, 1(5):649-683, 1994. ISSN 1370-1444.
17. Mercedes H. Rosas. The Kronecker product of Schur functions indexed by two-row shapes or hook shapes. J. Algebraic Combin., 14(2):153-173, 2001. ISSN 0925-9899.
18. Bruce E. Sagan. The symmetric group, volume 203 of Graduate Texts in Mathematics. Springer-Verlag, New York, second edition, 2001. ISBN 0-387-95067-2. Representations, combinatorial algorithms, and symmetric functions.
19. Richard P. Stanley. Enumerative combinatorics. Vol. 2, volume 62 of Cambridge Studies in Advanced Mathematics. Cambridge University Press, Cambridge, 1999. ISBN 0-521-56069-1; 0-521-78987-7. With a foreword by Gian-Carlo Rota and appendix 1 by Sergey Fomin.
20. V. Strassen. Rank and optimal computation of generic tensors. Linear Algebra Appl., 52/53:645-685, 1983. ISSN 0024-3795.
21. Leslie G. Valiant. The complexity of computing the permanent. Theoret. Comput. Sci., 8(2):189-201, 1979. ISSN 0304-3975.
22. Dominic J. A. Welsh. Complexity: knots, colourings and counting, volume 186 of London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge, 1993. ISBN 0-521-45740-8.