Q-counting rook configurations and a formula of frobenius

Journal of Combinatorial Theory, Series A - Tập 41 Số 2 - Trang 246-275 - 1986
Adriano M. Garsia1, Jeffrey B. Remmel1
1Department of Mathematics, University of California, San Diego, La Jolla, California 92093, USA

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Tài liệu tham khảo

Andrews, 1975, Identities in combinatorics III: A q-analog of the Lagrange inversion theorem, 53, 240

Foata, 1977, Distributions Euleriennes et Mahoniennes sur le groupe des permutations, 27

Foata, 1970, Theorie geometrique des polynomes Euleriens, Vol. 138

Garsia, 1980, On the maj and inv q-analogues of Eulerian polynomials, J. Linear Multilinear Alg., 8, 21, 10.1080/03081087908817296

Garsia, 1981, A q-analogue of the Lagrange inversion formula, Houston J. Math., 7, 205

Garsia, 1979, Permutation statistics and partitions, Adv. in Math., 31, 288, 10.1016/0001-8708(79)90046-X

Garsia, 1980, A combinatorial interpretation of the q-derangement and q-Laguerre numbers, European J. Combin., 1, 47, 10.1016/S0195-6698(80)80021-7

A. M. Garsia and J. Remmel, A novel form of q-Lagrange inversion, Houston J. Math., to appear.

Gessel, 1980, A non-commutative generalization and q-analogue of the Lagrange inversion formula, Trans. Amer. Math. Soc., 257, 455

Goldman, 1975, Rook Theory I, Rook equivalence of Ferrers boards, 52, 485

Goldman, 1976, Rook Theory II. Boards of binomial type, SIAM J. Appl. Math., 31, 618, 10.1137/0131055

Gould, 1961, The q-Stirling numbers of first and second kinds, Duke Math. J., 28, 281, 10.1215/S0012-7094-61-02826-5

Hahn, 1949, Uber orthogonalpolynome, die q-Differenzengleichungen genugen, Math. Nachr., 2, 4, 10.1002/mana.19490020103

Heilmann, 1972, Theory of monomer-dimer systems, Comm. Math. Phys., 25, 190, 10.1007/BF01877590

Milne, 1982, Restricted growth functions, rank row matchings of partition lattices and q-Stirling numbers, Adv. in Math., 43, 173, 10.1016/0001-8708(82)90032-9

Nijenhuis, 1976, On permanents and zeros of rook polynomials, J. Combin. Theory Ser. A, 21, 240, 10.1016/0097-3165(76)90068-6

Riordan, 1958