Another Involution Principle-Free Bijective Proof of Stanley's Hook-Content Formula

Journal of Combinatorial Theory. Series A

Volumn 88, Issue 1, 1999, Pages 66-92

  Krattenthaler, C ^a  

^a UNIVERSITY OF VIENNA   (Austria)

Author keywords

Bijection; Hook formula; Hook content formula; Jeu de taquin; Plane partitions; Tableaux

Indexed keywords

EID: 0141667341     PISSN: 00973165     EISSN: None     Source Type: Journal    
DOI: 10.1006/jcta.1999.2979     Document Type: Article

References (20)

1. C. J. Colbourn, W. J. Myrvold, and E. Neufeld, Two algorithms for unranking arborescences, J. Algorithms 20 (1996), 268-281.
2. J. S. Frame, G. B. Robinson, and R. M. Thrall, The hook graphs of the symmetric group, Canad. J. Math. 6 (1954), 316-325.
3. A. M. Garsia and S. C. Milne, Method for constructing bijections for classical partition identities, Proc. Nat. Acad. Sci. U.S.A. 78 (1981), 2026-2028.
4. A. P. Hillman and R. M. Grassl, Reverse plane partitions and tableau hook numbers, J. Combin. Theory Ser. A 21 (1976), 216-221.
5. C. Krattenthaler, An involution principle-free bijective proof of Stanley's hook-content formula, Discrete Math. Theoret. Comput. Sci. 3 (1998), 011-032.
6. M. Luby, D. Randall, and A. Sinclair, Markov chain algorithms for planar lattice structures (extended abstract), in "36th Annual Symposium on Foundations of Computer Science, 1995," pp. 150-159.
7. P. A. MacMahon, "Combinatory Analysis," Cambridge Univ. Press, Cambridge, UK, 1916; reprinted by Chelsea, New York, 1960.
8. J. C. Novelli, I. M. Pak, and A. V. Stoyanovskii, A direct bijective proof of the hook-length formula, Discrete Math. Theoret. Comput. Sdci 1 (1997), 53-67.
9. I. M. Pak and A. V. Stoyanovskii, A bijective proof of the hook-length formula and its analogues, Funktsional Anal. i Prilozhen. 26, No. 3 (1992), 80-82; English translation, Funct. Anal. Appl. 26 (1992), 216-218.
10. I. M. Pak and A. V. Stoyanovskii, A bijective proof of the hook-length formula and its analogues, Funktsional Anal. i Prilozhen. 26, No. 3 (1992), 80-82; English translation, Funct. Anal. Appl. 26 (1992), 216-218.
11. J. Propp, Generating random elements of finite distributive lattices, Electron. J. Combin. 4, No. 2 (1997), #R15.
12. J. Propp and D. B. Wilson, Exact sampling with coupled Markov chains and applications to statistical mechanics, Random Structures Algorithms 9 (1996), 223-252.
13. J. Propp and D. B. Wilson, Coupling from the past: A user's guide, in "Microsurveys in Discrete Probability" (D. Aldous and J. Propp, Eds.), DIMACS Ser. Discrete Math. Theoret. Comput. Sci., Vol.41, pp. 181-192, Amer. Math. Soc., Providence, 1998.
14. J. B. Remmel and R. Whitney, A bijective proof of the hook formula for the number of column-strict tableaux with bounded entries, European J. Combin. 4 (1983), 45-63.
15. D. P. Robbins, The story of 1, 2, 7, 42, 429, 7436, ..., Math. Intelligencer 13 (1991), 12-19.
16. B. E. Sagan, "The Symmetric Group," Wadsworth & Brooks/Cole, Pacific Grove, CA, 1991.
17. M.-P. Schützenberger, La correspondance de Robinson, in "Combinatoire et Représentation du Groupe Symétrique, Lecture Notes in Math., Vol. 579, pp. 59-113, Springer-Verlag, Berlin/Heidelberg/New York, 1977.
18. R. P. Stanley, Theory and applications of plane partitions, Part 2, Stud. Appl. Math. 50 (1971), 259-279.
19. D. B. Wilson, Determinant algorithms for random planar structures, in "Proceedings of the Eighth Annual ACM-SIAM Symposium on Discrete Algorithms, 1997," pp. 258-267.
20. D. B. Wilson, Mixing times of lozenge tiling and card shuffling Markov chains, manuscript in preparation.