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. == Definition == The star product of two graded posets ( P , ≤ P ) {\displaystyle (P,\leq _{P})} and ( Q , ≤ Q ) {\displaystyle (Q,\leq _{Q})} , where P {\displaystyle P} has a unique maximal element 1 ^ {\displaystyle {\widehat {1}}} and Q {\displaystyle Q} has a unique minimal element 0 ^ {\displaystyle {\widehat {0}}} , is a poset P ∗ Q {\displaystyle P*Q} on the set ( P ∖ { 1 ^ } ) ∪ ( Q ∖ { 0 ^ } ) {\displaystyle (P\setminus \{{\widehat {1}}\})\cup (Q\setminus \{{\widehat {0}}\})} .