Schubert calculus and Pieri's formula In the lecture notes  Grassmannians: the first example of a moduli space. MIT Open Course Ware. page 7:

Are there any formal publications (books/papers) where I can find the formula?
 A: Here you have some standard references (quoted in the comments):


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*Hiller, Howard. Geometry of Coxeter groups. Research Notes in Mathematics, 54. Pitman (Advanced Publishing Program), Boston, Mass.-London, 1982. iv+213 pp. ISBN: 0-273-08517-4 MR0649068 (83h:14045)

*Fulton, William. Young tableaux. With applications to representation theory and geometry. London Mathematical Society Student Texts, 35. Cambridge University Press, Cambridge, 1997. x+260 pp. ISBN: 0-521-56144-2; 0-521-56724-6 MR1464693 (99f:05119)

*Manivel, Laurent. Symmetric functions, Schubert polynomials and degeneracy loci. Translated from the 1998 French original by John R. Swallow. SMF/AMS Texts and Monographs, 6. Cours Spécialisés [Specialized Courses], 3. American Mathematical Society, Providence, RI; Société Mathématique de France, Paris, 2001. viii+167 pp. ISBN: 0-8218-2154-7 MR1852463 (2002h:05161)


Let me add another nice reference:


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*Hiller, Howard L. Schubert calculus of a Coxeter group. Enseign. Math. (2) 27 (1981), no. 1-2, 57--84. MR0630960 (82m:14031)


Hiller's paper is freely available online here.
