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:
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.
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