I want to filter the set of all connected posets with n points using sage. I want to filter out the posets whose underlying undirected graph of its Hasse diagram is not a tree (equivalently, the incidence algebra is not hereditary) and such that there is no element x in the poset P such that any other element of P is comparable to y. Is there an easy method to do this with sage?
Maybe something like this
sage: def banana(n):
....: for P in posets(n):
....: if not P.is_connected():
....: continue
....: H = P.hasse_diagram()
....: if H.to_undirected().is_tree():
....: continue
....: dg = H.transitive_closure()
....: if any(dg.degree(x) == n - 1 for x in dg):
....: continue
....: yield P
Asked: 2020-11-29 11:17:39 +0100
Seen: 189 times
Last updated: Nov 29 '20
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