Flag-symmetric and locally rank-symmetric partially ordered sets

@article{Stanley1996FlagsymmetricAL,
  title={Flag-symmetric and locally rank-symmetric partially ordered sets},
  author={Richard P. Stanley},
  journal={Electr. J. Comb.},
  year={1996},
  volume={3}
}
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

References

Publications referenced by this paper.
Showing 1-10 of 20 references

Multipartite P -partitions and inner products of skew Schur functions

I. Gessel
in Combinatorics and Algebra (C. Greene, ed.), Contemporary Math., vol. 34, American Mathematical Society, Providence, RI • 1984
View 3 Excerpts
Highly Influenced

Representations of primary arguesian lattices

B. J onsson, G. S. Monk
Pa- ci c J. Math • 1969
View 3 Excerpts
Highly Influenced

A survey of Eulerian posets

R. Stanley
Proc. NATO Advanced Study Institute on Polytopes: Abstract, Convex, and Computational • 1993
View 1 Excerpt

P-Partitions and the plactic congruence

Graphs and Combinatorics • 1993
View 1 Excerpt

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
View 2 Excerpts

A unimodality result in the enumeration of subgroups of a nite abelian group

L. M. Butler
Proc. Amer. Math. Soc. 101 • 1987
View 1 Excerpt

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

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