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References
M. F. Atiyah and I. G. Macdonald, Introduction to Commutative Algebra, Addison-Wesley, Reading, Mass., 1969.
E. A. Bender and D. E. Knuth, Enumeration of plane partitions, J. Combinatorial Theory 13 (1972), 40–54.
J. B. Carrell and D. I. Lieberman, Chern classes of the Grassmannians and the Schubert calculus, preprint.
P. Doubilet, G.-C. Rota, and J. Stein, On the foundations of combinatorial theory: IX, Combinatorial methods in invariant theory, Studies in Applied Math. 53 (1974), 185–216.
P. Hall, The algebra of partitions, Proc. 4th Canad. Math. Congr. Banff. 1957 (1959), 147–159.
M. Hochster, Rings of invariants of tori, Cohen-Macaulay rings generated by monomials, and polytones, Annals of Math. 96 (1972), 318–337.
W. V. D. Hodge and D. Pedoe, Methods of algebraic geometry, vols. I and II, Cambridge University Press, 1953.
G. Horrocks, On the relation of S-functions to Schubert varieties, Proc. London Math. Soc. (3) 7 (1957), 265–280.
S. L. Kleiman, Problem 15. Rigorous foundation of Schubert's enumerative calculus, to appear in the Proceedings of a Symposium on Mathematical Developments Arising from the Hilbert Problems, held at DeKalb, Illinois, May 13–17, 1974.
S. L. Kleiman and D. Laksov, Schubert calculus, Amer. Math. Monthly 79 (1972), 1061–1082.
D. E. Knuth, Permutations, matrices, and generalized Young tableaux, Pacific J. Math. 34 (1970), 709–727.
G. Kreweras, Sur une classe de problèmes de dénombrement liés au treillis des partitions des entiers, Cahiers du BURO 6 (1965).
A. Lascoux, Puissances extérieures, déterminants et cycles de Schubert, Bull. Soc. Math. France 102 (1974), 161–179.
A. Lascoux, Polynômes symétriques et coefficients d'intersection de cycles de Schubert, C. R. Acad. Sc. Paris, 279 A (1974), 201–204.
A. Lascoux, Fonctions de Schur et grassmanniennes, C. R. Acad. Sc. Paris 281 A (1975), 813–815, 851–854.
L. Lesieur, Les problèmes d'intersections sur une variété de Grassmann, C. R. Acad. Sc. Paris 225 (1947), 916–917.
D. E. Littlewood, The Theory of Group Characters, second ed., Oxford University Press, 1950.
P. A. MacMahon, Combinatory Analysis, vols. 1–2, Cambridge University Press, 1915, 1916; reprinted by Chelsea, New York, 1960.
G.-C. Rota, Combinatorial theory, old and new, Actes du Congres International des Mathématiciens (Nice, 1970), Gauthier-Villars, Paris, 1971, pp. 229–233.
M. Schützenberger, La correspondance de Robinson, in these Lecture Notes.
R. Stanley, Theory and application of plane partitions, Parts 1 and 2, Studies in Applied Math. 50 (1971), 167–188, 259–279.
R. Stanley, Ordered structures and partitions, Memoirs of the Amer. Math. Soc., no. 119, 1972.
R. Stanley, Combinatorial reciprocity theorems, Advances in Math. 14 (1974), 194–253.
R. Stanley, Hilbert functions of graded algebras, Advances in Math., to appear.
N. White, The bracket ring of a combinatorial geometry, I, Trans. Amer. Math. Soc. 202 (1975), 79–95.
N. White, The bracket ring of a combinatorial geometry, II: Unimodular geometries, Trans. Amer. Math. Soc. 214 (1975), 233–248.
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Stanley, R.P. (1977). Some combinatorial aspects of the Schubert calculus. In: Foata, D. (eds) Combinatoire et Représentation du Groupe Symétrique. Lecture Notes in Mathematics, vol 579. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0090019
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DOI: https://doi.org/10.1007/BFb0090019
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