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.


The star product of Eulerian posets is Eulerian.

See also


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