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Symmetric Functions

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A Course in Enumeration

Part of the book series: Graduate Texts in Mathematics ((GTM,volume 238))

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Abstract

The theory of symmetric functions provides an elegant algebraic framework for many enumeration problems, in particular, as we shall see, for plane partitions. As with generating functions they encode a great deal of information, and algebraic manipulations often provide stupendously simple proofs of seemingly difficult problems.

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Notes and References

  1. E.A. Bender and D.E. Knuth (1972): Enumeration of plane partitions. J. Combinatorial Theory 13, 225–245.

    Article  MathSciNet  Google Scholar 

  2. D.M. Bressoud (1999): Proofs and Confirmations. The Story of the Alternating Sign Matrix Conjecture. Cambridge Univ. Press, Cambridge.

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  3. J.S. Frame, G. de B. Robinson, and R.M. Thrall (1954): The hook graphs of S n. Canad. J. Math. 6, 316–324.

    MATH  MathSciNet  Google Scholar 

  4. C. Greene, A. Nijenhuis, and H.S. Wilf (1979): A probabilistic proof of a formula for the number of Young tableaux of a given shape. Advances Math. 31, 104–109.

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  5. D.E. Knuth (1970): Permutations, matrices, and generalized Young tableaux. Pacific J. Math. 34, 709–727.

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  6. I.G. Macdonald (1995): Symmetric Functions and Hall Polynomials, 2nd edition. Oxford Univ. Press, Oxford.

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  7. P.A. MacMahon (1915): Combinatory Analysis, 2 vols. Cambridge Univ. Press, Cambridge; reprinted in one volume by Chelsea, New York, 1960.

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  8. G. de B. Robinson (1938): On representations of S n. Amer. J. Math. 60, 745–760.

    Article  MATH  MathSciNet  Google Scholar 

  9. C.E. Schensted (1961): Longest increasing and decreasing subsequences. Canad. J. Math. 13, 179–191.

    MATH  MathSciNet  Google Scholar 

  10. R.P. Stanley (1999): Enumerative Combinatorics, vol. 2. Cambridge Univ. Press, Cambridge.

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© 2007 Springer-Verlag Berlin Heidelberg

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(2007). Symmetric Functions. In: A Course in Enumeration. Graduate Texts in Mathematics, vol 238. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-39035-0_9

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