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- The term "Star product" may also refer to the Moyal product.
In mathematics, 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.
The star product of Eulerian posets is Eulerian.
- Stanley, R., Flag -vectors and the -index, Math. Z. 216 (1994), 483-499.