Inmathematics, the star product is a method of combining graded posets with unique minimal and maximal elements, preserving the property that the posets are Eulerian.
The star product of two graded posets and
, where
has a unique maximal element
and
has a unique minimal element
, is a poset
on the set
. We define the partial order
by
if and only if:
In other words, we pluck out the top of and the bottom of
, and require that everything in
be smaller than everything in
.
For example, suppose and
are the Boolean algebra on two elements.
Then is the poset with the Hasse diagram below.
The star product of Eulerian posets is Eulerian.
This article incorporates material from star product on PlanetMath, which is licensed under the Creative Commons Attribution/Share-Alike License.
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