Flag Vectors of Eulerian Partially Ordered Sets

The closed cone of flag vectors of Eulerian partially ordered sets is studied. A new family of linear inequalities valid for Eulerian flag vectors is given. Half-Eulerian posets are defined. Certain limit posets of Billera and Hetyei are half-Eulerian; they give rise to extreme rays of the cone for Eulerian posets. Other extreme posets are formed from consideration of the cd -index. The cone of Eulerian flag vectors is completely determined up through rank seven.

[1]  Louis J. Billera,et al.  Noncommutative Enumeration in Graded Posets , 2000 .

[2]  Louis J. Billera,et al.  Decompositions of Partially Ordered Sets , 2000, Order.

[3]  M. Bayer.  SIGNS IN THE cd-INDEX OF EULERIAN PARTIALLY ORDERED SETS , 2000, math/0001053.

[4]  Louis J. Billera,et al.  Linear Inequalities for Flags in Graded Partially Ordered Sets , 2000, J. Comb. Theory, Ser. A.

[5]  Louis J. Billera,et al.  Neighborly cubical spheres and a cubical lower bound conjecture , 1997 .

[6]  Richard Ehrenborg,et al.  Thec-2d-Index of Oriented Matroids , 1997, J. Comb. Theory, Ser. A.

[7]  R. Stanley.  Flagf-vectors and thecd-index , 1994 .

[8]  Richard P. Stanley,et al.  A Survey of Eulerian Posets , 1994 .

[9]  Peter McMullen,et al.  Polytopes: Abstract, Convex and Computational , 1994 .

[10]  B. Sturmfels.  Oriented Matroids , 1993 .

[11]  Andrew Klapper,et al.  A new index for polytopes , 1991, Discret. Comput. Geom..

[12]  Gil Kalai,et al.  A new basis of polytopes , 1988, J. Comb. Theory, Ser. A.

[13]  Margaret Bayer,et al.  The extended f-vectors of 4-polytopes , 1987, J. Comb. Theory, Ser. A.

[14]  Louis J. Billera,et al.  Generalized Dehn-Sommerville relations for polytopes, spheres and Eulerian partially ordered sets , 1985 .

[15]  Anders Björner,et al.  Posets, Regular CW Complexes and Bruhat Order , 1984, Eur. J. Comb..

[16]  Richard P. Stanley,et al.  Some Aspects of Groups Acting on Finite Posets , 1982, J. Comb. Theory, Ser. A.

[17]  Richard P. Stanley,et al.  Balanced Cohen-Macaulay complexes , 1979 .

[18]  Jim Lawrence,et al.  Oriented matroids , 1978, J. Comb. Theory B.

[19]  P. M. Cohn,et al.  On subsemigroups of free semigroups , 1962 .