def _yang_baxter_graph(self): r""" Construct and cache the underlying Yang-Baxter graph. EXAMPLES:: sage: rho = SymmetricGroupRepresentation([3,2], 'specht') sage: rho._yang_baxter_graph Yang-Baxter graph of [3, 2], with top vertex (1, 0, 2, 1, 0) """ return YangBaxterGraph_partition(self._partition)
def _yang_baxter_graph(self): r""" Return the Yang-Baxter graph associated with the representation, with vertices labelled by the vector of contents of the partition. EXAMPLES:: sage: orth = SymmetricGroupRepresentation([3,2], "orthogonal") sage: orth._yang_baxter_graph Yang-Baxter graph of [3, 2], with top vertex (0, -1, 2, 1, 0) """ Y = YangBaxterGraph_partition(self._partition) n = self._partition.size() # relabel vertices with "vector of contents" Y.relabel_vertices(\ partition_to_vector_of_contents(self._partition, reverse=True)) # relabel edges with "differences" edge_relabel_dict = {} for (u, v, op) in Y.edges(): i = op.position() + 1 edge_relabel_dict[u, v] = (n - i, QQ((1, u[i] - u[i - 1]))) Y.relabel_edges(edge_relabel_dict) return Y
def _yang_baxter_graph(self): r""" Return the Yang-Baxter graph associated with the representation, with vertices labelled by the vector of contents of the partition. EXAMPLES:: sage: orth = SymmetricGroupRepresentation([3,2], "orthogonal") sage: orth._yang_baxter_graph Yang-Baxter graph of [3, 2], with top vertex (0, -1, 2, 1, 0) """ Y = YangBaxterGraph_partition(self._partition) n = self._partition.size() # relabel vertices with "vector of contents" Y.relabel_vertices(partition_to_vector_of_contents(self._partition, reverse=True)) # relabel edges with "differences" edge_relabel_dict = {} for (u, v, op) in Y.edges(): i = op.position() + 1 edge_relabel_dict[u, v] = (n - i, QQ((1, u[i] - u[i - 1]))) Y.relabel_edges(edge_relabel_dict) return Y