The poset $P$ is Eulerian if every non-trivial closedInterval of $P$ has an equal number of vertices of even and odd rank.
The $n$ chain is non-Eulerian for $n \geq 3$.
i1 : isEulerian chain 10 o1 = false |
The facePoset of the simplicialComplex of an $n$ cycle is Eulerian.
i2 : n = 10; |
i3 : R = QQ[x_0..x_(n-1)]; |
i4 : F = facePoset simplicialComplex apply(n, i -> x_i * x_((i+1)%n)); |
i5 : isEulerian F o5 = true |