The Weak Order and Flag h - Vector Inequalities May 2005
نویسندگان
چکیده
The following paper examines properties of the weak order on the groups Sr+1 and Br+1 as motivated by the search for a combinatorial proof of known h-vector inequalities. Several general results are developed with respect to descent set domination, and an explanation of the computer programs used to generate a number of these results is presented. While this paper primarily focuses on hand flag h-vector inequalities of the order complex of geometric lattices, such inequalities for the order complexes of distributive and supersolvable lattices are also explored. Finally, several courses of action for further study are considered.
منابع مشابه
Inequalities for the H- and Flag H-vectors of Geometric Lattices
We prove that the order complex of a geometric lattice has a convex ear decomposition. As a consequence, if ∆(L) is the order complex of a rank (r+1) geometric lattice L, then the for all i ≤ r/2 the h-vector of ∆(L) satisfies, hi−1 ≤ hi and hi ≤ hr−i. We also obtain several inequalities for the flag h-vector of ∆(L) by analyzing the weak Bruhat order of the symmetric group. As an application, ...
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