Applications of Symmetric Functions to Cycle and Increasing Subsequence Structure after Shuffles

Springer Science and Business Media LLC - Tập 16 - Trang 165-194 - 2002
Jason Fulman1
1Department of Mathematics, University of Pittsburgh, Pittsburgh, USA

Tóm tắt

Using symmetric function theory, we study the cycle structure and increasing subsequence structure of permutations after iterations of various shuffling methods. We emphasize the role of Cauchy type identities and variations of the Robinson-Schensted-Knuth correspondence.

Tài liệu tham khảo

D. Aldous and P. Diaconis, “Shuffling cards and stopping times,” Amer. Math. Monthly 93 (1986), 333–348.

A. Erdei, “Proof of a conjecture of Schoenburg on the generating function of a totally positive sequence,” Canad. J. Math 5 (1953), 86–94.

S. Lalley, “Riffle shuffles and their associated dynamical systems,” J. Theoret. Probab. 12 (1999), 903–932.

I. Macdonald, Symmetric Functions and Hall polynomials, 2nd edition, Clarendon Press, Oxford, 1995.

C. Reutenauer, Free Lie Algebras, London Mathematical Society Monographs. New Series 7. Clarendon Press and Oxford University Press, New York, 1993.

B. Sagan, The Symmetric Group. Representations, Combinatorial Algorithms, and Symmetric Functions, 2nd edition, Springer-Verlag, New York, 2001.

S. Shnider and S. Sternberg, Quantum Groups. Graduate Texts in Mathematical Physics, II. International Press, 1993.

R. Stanley, Enumerative Combinatorics, Vol. 2, Cambridge University Press, New York/Cambridge, 1999.