Star product
From Wikipedia, the free encyclopedia
In mathematics, the star product of two graded posets 
and 
, where P has a unique maximal element 
and Q has a unique minimal element 
, is a poset P * Q on the set 
. We define the partial order 
by 
if and only if:
- 1.
, and 
; - 2.
, and 
; or - 3.
and 
.
In other words, we pluck out the top of P and the bottom of Q, and require that everything in P be smaller than everything in Q. For example, suppose P and Q are the Boolean algebra on two elements.
Then P * Q is the poset with the Hasse diagram below.
The star product of Eulerian posets is Eulerian.
[edit] Bibliography
- Stanley, R., Flag f-vectors and the
-index, Math. Z. 216 (1994), 483-499.
This article incorporates material from star product on PlanetMath, which is licensed under the GFDL.
