365 research outputs found
A Family of Partially Ordered Sets with Small Balance Constant
Given a finite poset and two distinct elements and , we
let denote the fraction of linear
extensions of in which precedes . The balance constant
of is then defined by The
- conjecture asserts that whenever
is not a chain, but except from certain trivial examples it is not
known when equality occurs, or even if balance constants can approach .
In this paper we make some progress on the conjecture by exhibiting a
sequence of posets with balance constants approaching
, answering a question of
Brightwell. These provide smaller balance constants than any other known
nontrivial family.Comment: 11 pages, 4 figure
The flag f-vectors of Gorenstein* order complexes of dimension 3
We characterize the cd-indices of Gorenstein* posets of rank 5, equivalently
the flag f-vectors of Gorenstein* order complexes of dimension 3. As a
corollary, we characterize the f-vectors of Gorenstein* order complexes in
dimensions 3 and 4. This characterization rise a speculated intimate connection
between the f-vectors of flag homology spheres and the f-vectors of Gorenstein*
order complexes
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