Star product

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 alsoEdit


  • Stanley, R., Flag  -vectors and the  -index, Math. Z. 216 (1994), 483-499.

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