For every finite graded poset P with 0̂ and 1̂ we associate a certain formal power series FP (x) = FP (x1, x2, . . .) which encodes the flag f -vector (or flag h-vector) of P . A relative version FP/Γ is also defined, where Γ is a subcomplex of the order complex of P . We are interested in the situation where FP or FP/Γ is a symmetric function of x1, x2, . . .. When FP or FP/Γ is symmetric we consider its expansion in terms of various symmetric function bases, especially the Schur functions… CONTINUE READING

Produits et coproduits des fonctions quasi-sym etriques et de l'alg ebre des descentes

C. Malvenuto

Ph.D. thesis, Universit e du Qu ebec a Montr eal, Novem- ber • 1993

Re ection Groups and Coxeter Groups

J. E. Humphreys

Cambridge University Press, Cambridge • 1990

Local stationary algebras

A. M. Vershik

Amer. Math. Soc. Transl. (2) 148 (1991), 1{13; translated from Proc. First Siberian Winter School \Algebra and Analysis" • 1988

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L. M. Butler

Proc. Amer. Math. Soc. 101 • 1987

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Generalized h-vectors

R. Stanley

intersection cohomology of toric varieties, and related results, in Commutative Algebra and Combinatorics (M. Nagata and H. Matsumura, eds.), Advanced Studies in Pure Mathematics 11, Kinokuniya, Tokyo, and North-Holland, Amsterdam/New York • 1987