def PentagonPoset(facade = None): """ Returns the Pentagon poset. INPUT: - ``facade`` (boolean) -- whether to make the returned poset a facade poset (see :mod:`sage.categories.facade_sets`). The default behaviour is the same as the default behaviour of the :func:`~sage.combinat.posets.posets.Poset` constructor). EXAMPLES:: sage: P = Posets.PentagonPoset(); P Finite lattice containing 5 elements sage: P.cover_relations() [[0, 1], [0, 2], [1, 4], [2, 3], [3, 4]] This is smallest lattice that is not modular:: sage: P.is_modular() False This poset and the :meth:`DiamondPoset` are the two smallest lattices which are not distributive:: sage: P.is_distributive() False sage: Posets.DiamondPoset(5).is_distributive() False """ p = LatticePoset([[1,2],[4],[3],[4],[]], facade = facade) p.hasse_diagram()._pos = {0:[2,0],1:[0,2],2:[3,1],3:[3,3],4:[2,4]} return p
def PentagonPoset(facade=False): """ Returns the "pentagon poset". EXAMPLES:: sage: P = Posets.PentagonPoset(); P Finite lattice containing 5 elements sage: P.cover_relations() [[0, 1], [0, 2], [1, 4], [2, 3], [3, 4]] This lattice and the diamond poset on 5 elements are the two smallest lattices which are not distributive:: sage: P.is_distributive() False sage: Posets.DiamondPoset(5).is_distributive() False """ p = LatticePoset([[1, 2], [4], [3], [4], []], facade=facade) p.hasse_diagram()._pos = { 0: [2, 0], 1: [0, 2], 2: [3, 1], 3: [3, 3], 4: [2, 4] } return p
def PentagonPoset(facade = False): """ Returns the "pentagon poset". EXAMPLES:: sage: P = Posets.PentagonPoset(); P Finite lattice containing 5 elements sage: P.cover_relations() [[0, 1], [0, 2], [1, 4], [2, 3], [3, 4]] This lattice and the diamond poset on 5 elements are the two smallest lattices which are not distributive:: sage: P.is_distributive() False sage: Posets.DiamondPoset(5).is_distributive() False """ p = LatticePoset([[1,2],[4],[3],[4],[]], facade = facade) p.hasse_diagram()._pos = {0:[2,0],1:[0,2],2:[3,1],3:[3,3],4:[2,4]} return p