×

zbMATH — the first resource for mathematics

The Hillman-Grassl correspondence and the enumeration of reverse plane partitions. (English) Zbl 0474.05008

MSC:
05A15 Exact enumeration problems, generating functions
05A17 Combinatorial aspects of partitions of integers
PDF BibTeX XML Cite
Full Text: DOI
References:
[1] Andrews, G.E, Plane partitions (I): the macmahon conjecture, () · Zbl 0462.10010
[2] Bender, E.A; Knuth, D.E, Enumeration of plane partitions, J. combinatorial theory A, 13, 40-54, (1972) · Zbl 0246.05010
[3] Burge, W.H, Four correspondences between graphs and generalized Young tableaux, J. combinatorial theory A, 17, 12-30, (1974) · Zbl 0286.05115
[4] Frame, J.S; Robinson, G.de B; Thrall, R.M, The hook graphs of the symmetric group, Canad. J. math., 6, 316-325, (1954) · Zbl 0055.25404
[5] Gansner, E.R, Matrix correspondences and the enumeration of plane partitions, () · Zbl 0432.05010
[6] \scE. R. Gansner, Matrix correspondences of plane partitions, Pacific J. Math., in press. · Zbl 0432.05010
[7] \scE. R. Gansner, The enumeration of plane partitions via the Burge correspondence, preprint. · Zbl 0452.05004
[8] Hillman, A.P; Grassl, R.M, Reverse plane partitions and tableau hook numbers, J. combinatorial theory A, 21, 216-221, (1976) · Zbl 0341.05008
[9] Hillman, A.P; Grassl, R.M, Functions on tableau frames, Discrete math., 25, 245-255, (1979) · Zbl 0402.05006
[10] Knuth, D.E, Permutations, matrices and generalized Young tableaux, Pacific J. math., 34, 709-727, (1970) · Zbl 0199.31901
[11] Knuth, D.E, ()
[12] MacMahon, P.A, (), reprinted by Chelsea, New York, 1960
[13] Nakayama, T; Nakayama, T, On some modular properties of irreducible representations of a symmetric group I, II, Japan. J. math., Japan. J. math., 17, 411-423, (1940) · Zbl 0061.04001
[14] Rutherford, D.E, On certain numerical coefficients associated with partitions, (), 215-219 · Zbl 0147.26503
[15] Sagan, B.E, Partially ordered sets with hooklengths—an algorithmic approach, ()
[16] Schensted, C, Longest increasing and decreasing subsequences, Canad. J. math., 13, 179-191, (1961) · Zbl 0097.25202
[17] Stanley, R.P, Ordered structures and partitions, () · Zbl 0246.05007
[18] Stanley, R.P, Theory and applications of plane partitions II, Studies in applied math., 50, 259-279, (1971) · Zbl 0225.05012
[19] Stanley, R.P, Ordered structures and partitions, () · Zbl 0246.05007
[20] Thrall, R.M, A combinatorial problem, Mich. math. J., 1, 81-88, (1952) · Zbl 0049.01001
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.