On the number of rim hook tableaux
Rent the article at a discountRent now
* Final gross prices may vary according to local VAT.Get Access
A hooklength formula for the number of rim hook tableaux is used to obtain an inequality relating the number of rim hook tableaux of a given shape to the number of standard Young tableaux of the same shape. This provides an upper bound for a certain family of characters of the symmetric group. The analogues for shifted shapes and rooted trees are also given. Bibliography: 13 titles.
- P. Diaconis and M. Shahshahani, “Generating a random permutation with random transpositions,”Z. Wahrscheinlichkeitstheorie verw. Gebiete,57, 159–179 (1981). CrossRef
- S. Fomin and D. Stanton, “Rim hook lattices,” Report No. 23 (1991/92), Institut Mittag-Leffler (1992).
- J. S. Frame, G. de B. Robinson, and R. M. Thrall, “The hook graphs of the symmetric group,”Canad. J. Math.,6, 316–324 (1954).
- G. James and A. Kerber, “The representation theory of the symmetric group,” in:Encyclopedia of Mathematics and Its Applications, Vol. 16, G.-C. Rota (ed.), Addison-Wesley, Reading, MA (1981).
- N. Lulov,Random Walks on the Symmetric Group generated by Conjugacy Classes, Ph. D. Thesis, Harverd University (1996).
- I. G. Macdonald,Symmetric Functions and Hall Polynomials, Oxford University Press (1979).
- A. O. Morris and A. K. Yasseen, “Some combinatorial results involving shifted Young diagrams,”Math. Proc. Camb. Phil. Soc.,99, 23–31 (1986).
- G. de B. Robinson,Representation Theory of the Symmetric Group, University of Toronto Press (1961).
- B. E. Sagan, “The ubiquitous Young tableaux,” in:Invariant Theory and Young Tableaux, D. Stanton (ed.), Springer-Verlag (1990), pp. 262–298.
- B. E. Sagan,The Symmetric Group: Representations, Combinatorial Algorithms and Symmetric Functions, Wadsworth and Brooks/Cole (1991).
- R. P. Stanley, “The stable behaviour of some characters ofSL(n,ℂ),”Lin. Multilin. Algebra,16 3–27 (1984).
- J. Stembridge, “Canonical bases and self-evacuating tableaux,” Preprint.
- D. W. Stanton and D. E. White, “A Schensted algorithm for rim hook tableaux,”J. Combin. Theory. Ser. A,40 211–247 (1985).
- On the number of rim hook tableaux
Journal of Mathematical Sciences
Volume 87, Issue 6 , pp 4118-4123
- Cover Date
- Print ISSN
- Online ISSN
- Kluwer Academic Publishers-Plenum Publishers
- Additional Links
- Industry Sectors