Permutation statistics and partitions

Advances in Mathematics - Tập 31 - Trang 288-305 - 1979
A.M Garsia1, I Gessel1
1Department of Mathematics, University of California, San Diego, La Jolla, California 92037 USA

Tài liệu tham khảo

Andrews, 1976, The theory of partitions, Vol. 2 Carlitz, 1966, Permutations and sequences with repetitions by number of increases, J. Combinatorial Theory, 1, 350, 10.1016/S0021-9800(66)80057-1 Foata, 1977, Distributions Euleriennes et Mahoniennes sur le groupe des permutations, 27 D. Foata and M. P. Schutzenberger, Major index and inversion number of permutations, Math. Nachr., in press. A. M. Garsia, On the “maj” and “inv” q-analogues of Eulerian polynomials, J. Linear Multilinear Algebra, in press. Gessel, 1977, Generating functions and enumeration of sequences Gordon, 1963, Two theorems on multipartite partitions, J. London Math. Soc., 38, 459, 10.1112/jlms/s1-38.1.459 Knuth, 1970, A note on solid partitions, Math. Comp., 24, 955, 10.1090/S0025-5718-1970-0277401-7 Mahon, 1916 Mahon, 1960 Roselle, 1974, Coefficients associated with the expansion of certain products, 46, 144 Riordan, 1958 Stanley, 1972, Ordered structures and partitions, Mem. Amer. Math. Soc., 119 Stanley, 1973, The conjugate trace and trace of a plane partition, J. Combinatorial Theory, 14, 53, 10.1016/0097-3165(73)90063-0 Stanley, 1976, Binomial posets Moebius inversion and permutation enumeration, J. Combinatorial Theory Ser. A, 20, 336, 10.1016/0097-3165(76)90028-5