Algebraic Combinatorics pp 103-133 | Cite as

# A Glimpse of Young Tableaux

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## Abstract

We defined in Chap. 6 Young’s lattice *Y*, the poset of all partitions of all nonnegative integers, ordered by containment of their Young diagrams.

## Keywords

Standard Young Tableaux Young Diagram Walk Counts Graded Poset Hasse Diagram
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## References

- 5.E.A. Beem, Craige and Irene Schensted don’t have a car in the world, in
*Maine Times*(1982), pp. 20–21Google Scholar - 6.E.A. Bender, D.E. Knuth, Enumeration of plane partitions. J. Comb. Theor.
**13**, 40–54 (1972)MathSciNetzbMATHCrossRefGoogle Scholar - 36.S. Fomin, Duality of graded graphs. J. Algebr. Combin.
**3**, 357–404 (1994)zbMATHCrossRefGoogle Scholar - 37.S. Fomin, Schensted algorithms for dual graded graphs. J. Algebr. Combin.
**4**, 5–45 (1995)zbMATHCrossRefGoogle Scholar - 38.J.S. Frame, G. de B. Robinson, R.M. Thrall, The hook graphs of
*S*_{n}. Can. J. Math.**6**316–324 (1954)Google Scholar - 39.D.S. Franzblau, D. Zeilberger, A bijective proof of the hook-length formula. J. Algorithms
**3**, 317–343 (1982)MathSciNetzbMATHCrossRefGoogle Scholar - 41.F.G. Frobenius, Über die Charaktere der symmetrischen Gruppe, in
*Sitzungsber. Kön. Preuss. Akad. Wissen. Berlin*(1900), pp. 516–534;*Gesammelte Abh. III*, ed. by J.-P. Serre (Springer, Berlin, 1968), pp. 148–166Google Scholar - 42.W.E. Fulton,
*Young Tableaux*. Student Texts, vol. 35 (London Mathematical Society/Cambridge University Press, Cambridge, 1997)Google Scholar - 48.C. Greene, A. Nijenhuis, H.S. Wilf, A probabilistic proof of a formula for the number of Young tableaux of a given shape. Adv. Math.
**31**, 104–109 (1979)MathSciNetzbMATHCrossRefGoogle Scholar - 57.A.P. Hillman, R.M. Grassl, Reverse plane partitions and tableaux hook numbers. J. Comb. Theor. A
**21**, 216–221 (1976)MathSciNetzbMATHCrossRefGoogle Scholar - 64.C. Krattenthaler, Bijective proofs of the hook formulas for the number of standard Young tableaux, ordinary and shifted. Electronic J. Combin.
**2**, R13, 9 pp. (1995)Google Scholar - 65.D.E. Knuth, Permutations, matrices, and generalized Young tableaux. Pac. J. Math.
**34**, 709–727 (1970)MathSciNetzbMATHCrossRefGoogle Scholar - 73.P.A. MacMahon, Memoir on the theory of the partitions of numbers — Part I. Philos. Trans. R. Soc. Lond. A
**187**, 619–673 (1897);*Collected Works*, vol. 1, ed. by G.E. Andrews (MIT, Cambridge, 1978), pp. 1026–1080Google Scholar - 74.P.A. MacMahon, Memoir on the theory of the partitions of numbers — Part IV. Philos. Trans. R. Soc. Lond. A
**209**, 153–175 (1909);*Collected Works*, vol. 1, ed. by G.E. Andrews (MIT, Cambridge, 1978), pp. 1292–1314Google Scholar - 75.P.A. MacMahon,
*Combinatory Analysis*, vols. 1, 2 (Cambridge University Press, Cambridge, 1915/1916); Reprinted in one volume by Chelsea, New York, 1960Google Scholar - 80.J.-C. Novelli, I. Pak, A.V. Stoyanovskii, A new proof of the hook-length formula. Discrete Math. Theor. Comput. Sci.
**1**, 053–067 (1997)MathSciNetGoogle Scholar - 93.J.B. Remmel, Bijective proofs of formulae for the number of standard Young tableaux. Linear Multilinear Algebra
**11**, 45–100 (1982)MathSciNetzbMATHCrossRefGoogle Scholar - 94.
- 96.B.E. Sagan,
*The Symmetric Group*, 2nd edn. (Springer, New York, 2001)zbMATHCrossRefGoogle Scholar - 97.C.E. Schensted, Longest increasing and decreasing subsequences. Can. J. Math.
**13**, 179–191 (1961)MathSciNetzbMATHCrossRefGoogle Scholar - 104.R. Stanley, Differential posets. J. Am. Math. Soc.
**1**, 919–961 (1988)MathSciNetzbMATHCrossRefGoogle Scholar - 106.R. Stanley, Variations on differential posets, in
*Invariant Theory and Tableaux*, ed. by D. Stanton. The IMA Volumes in Mathematics and Its Applications, vol. 19 (Springer, New York, 1990), pp. 145–165Google Scholar - 107.R. Stanley,
*Enumerative Combinatorics*, vol. 1, 2nd edn. (Cambridge University Press, Cambridge, 2012)Google Scholar - 108.R. Stanley,
*Enumerative Combinatorics*, vol. 2 (Cambridge University Press, New York, 1999)CrossRefGoogle Scholar - 120.M.A.A. van Leeuwen, The Robinson-Schensted and Schützenberger algorithms, Part 1: new combinatorial proofs, Preprint no. AM-R9208 1992, Centrum voor Wiskunde en Informatica, 1992Google Scholar
- 122.A. Young, Qualitative substitutional analysis (third paper). Proc. Lond. Math. Soc. (2)
**28**, 255–292 (1927)Google Scholar

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