next | previous | forward | backward | up | top | index | toc | Macaulay2 web site
Posets :: isEulerian(Poset)

isEulerian(Poset) -- determines if a ranked poset is Eulerian

Synopsis

Description

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 ≥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

See also