In mathematics, 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:
- 1. , and ;
- 2. , and ; or
- 3. and .
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.