Generalizations of Cauchy’s summation theorem for Schur functions

Andrews, G. E.; Goulden, I. P.; Jackson, D. M.

doi:10.1090/S0002-9947-1988-0973178-8

Generalizations of Cauchy’s summation theorem for Schur functions
HTML articles powered by AMS MathViewer

by G. E. Andrews, I. P. Goulden and D. M. Jackson

Trans. Amer. Math. Soc. 310 (1988), 805-820

DOI: https://doi.org/10.1090/S0002-9947-1988-0973178-8

PDF | Request permission

Abstract:

Cauchy’s summation theorem for Schur functions is generalized, and a number of related results are given. The result is applied to a combinatorial problem involving products of pairs of permuations, by appeal to properties of the group algebra of the symmetric group.

References

Eiichi Bannai and Tatsuro Ito, Algebraic combinatorics. I, The Benjamin/Cummings Publishing Co., Inc., Menlo Park, CA, 1984. Association schemes. MR 882540

Group theory in statistics

Ira M. Gessel, Counting three-line Latin rectangles, Combinatoire énumérative (Montreal, Que., 1985/Quebec, Que., 1985) Lecture Notes in Math., vol. 1234, Springer, Berlin, 1986, pp. 106–111. MR 927761, DOI 10.1007/BFb0072512
I. P. Goulden and D. M. Jackson, Combinatorial enumeration, Wiley-Interscience Series in Discrete Mathematics, John Wiley & Sons, Inc., New York, 1983. With a foreword by Gian-Carlo Rota. MR 702512
D. M. Jackson, Counting cycles in permutations by group characters, with an application to a topological problem, Trans. Amer. Math. Soc. 299 (1987), no. 2, 785–801. MR 869231, DOI 10.1090/S0002-9947-1987-0869231-9
I. G. Macdonald, Symmetric functions and Hall polynomials, Oxford Mathematical Monographs, The Clarendon Press, Oxford University Press, New York, 1979. MR 553598
Gian-Carlo Rota, The number of partitions of a set, Amer. Math. Monthly 71 (1964), 498–504. MR 161805, DOI 10.2307/2312585
C. Schensted, Longest increasing and decreasing subsequences, Canadian J. Math. 13 (1961), 179–191. MR 121305, DOI 10.4153/CJM-1961-015-3

Bestimmung der symmetrischen Verbindungen Vermittelst ihrer erzeugenden Funktion