def from_expr(l): """ Returns a RibbonTableau from a MuPAD-Combinat expr for a skew tableau. The first list in expr is the inner shape of the skew tableau. The second list are the entries in the rows of the skew tableau from bottom to top. Provided primarily for compatibility with MuPAD-Combinat. EXAMPLES:: sage: import sage.combinat.ribbon_tableau as ribbon_tableau sage: sage.combinat.ribbon_tableau.from_expr([[1,1],[[5],[3,4],[1,2]]]) [[None, 1, 2], [None, 3, 4], [5]] sage: type(_) <class 'sage.combinat.ribbon_tableau.RibbonTableau_class'> """ return RibbonTableau_class(skew_tableau.from_expr(l)._list)
def insertion_tableau(skp, perm, evaluation, tableau, length): """ INPUT: - ``skp`` - skew partitions - ``perm, evaluation`` - non-negative integers - ``tableau`` - skew tableau - ``length`` - integer TESTS:: sage: from sage.combinat.ribbon_tableau import insertion_tableau sage: insertion_tableau([[1], []], [1], 1, [[], []], 1) [[], [[1]]] sage: insertion_tableau([[2, 1], []], [1, 1], 2, [[], [[1]]], 1) [[], [[2], [1, 2]]] sage: insertion_tableau([[2, 1], []], [0, 0], 3, [[], [[2], [1, 2]]], 1) [[], [[2], [1, 2]]] sage: insertion_tableau([[1, 1], []], [1], 2, [[], [[1]]], 1) [[], [[2], [1]]] sage: insertion_tableau([[2], []], [0, 1], 2, [[], [[1]]], 1) [[], [[1, 2]]] sage: insertion_tableau([[2, 1], []], [0, 1], 3, [[], [[2], [1]]], 1) [[], [[2], [1, 3]]] sage: insertion_tableau([[1, 1], []], [2], 1, [[], []], 2) [[], [[1], [0]]] sage: insertion_tableau([[2], []], [2, 0], 1, [[], []], 2) [[], [[1, 0]]] sage: insertion_tableau([[2, 2], []], [0, 2], 2, [[], [[1], [0]]], 2) [[], [[1, 2], [0, 0]]] sage: insertion_tableau([[2, 2], []], [2, 0], 2, [[], [[1, 0]]], 2) [[], [[2, 0], [1, 0]]] sage: insertion_tableau([[2, 2], [1]], [3, 0], 1, [[], []], 3) [[1], [[1, 0], [0]]] """ psave = partition.Partition(skp[1]) partc = skp[1] + [0] * (len(skp[0]) - len(skp[1])) tableau = skew_tableau.SkewTableau(expr=tableau).to_expr()[1] for k in range(len(tableau)): tableau[-(k + 1)] += [0] * (skp[0][k] - partc[k] - len(tableau[-(k + 1)])) ## We construct a tableau from the southwest corner to the northeast one tableau = [[0] * (skp[0][k] - partc[k]) for k in reversed(range(len(tableau), len(skp[0])))] + tableau tableau = skew_tableau.from_expr([skp[1], tableau]).conjugate() tableau = tableau.to_expr()[1] skp = skew_partition.SkewPartition(skp).conjugate().to_list() skp[1].extend([0] * (len(skp[0]) - len(skp[1]))) if len(perm) > len(skp[0]): return None for k in range(len(perm)): if perm[-(k + 1)] != 0: tableau[len(tableau) - len(perm) + k][skp[0][len(perm) - (k + 1)] - skp[1][len(perm) - (k + 1)] - 1] = evaluation return skew_tableau.SkewTableau( expr=[psave.conjugate(), tableau]).conjugate().to_expr()
def insertion_tableau(skp, perm, evaluation, tableau, length): """ INPUT: - ``skp`` - skew partitions - ``perm, evaluation`` - non-negative integers - ``tableau`` - skew tableau - ``length`` - integer TESTS:: sage: from sage.combinat.ribbon_tableau import insertion_tableau sage: insertion_tableau([[1], []], [1], 1, [[], []], 1) [[], [[1]]] sage: insertion_tableau([[2, 1], []], [1, 1], 2, [[], [[1]]], 1) [[], [[2], [1, 2]]] sage: insertion_tableau([[2, 1], []], [0, 0], 3, [[], [[2], [1, 2]]], 1) [[], [[2], [1, 2]]] sage: insertion_tableau([[1, 1], []], [1], 2, [[], [[1]]], 1) [[], [[2], [1]]] sage: insertion_tableau([[2], []], [0, 1], 2, [[], [[1]]], 1) [[], [[1, 2]]] sage: insertion_tableau([[2, 1], []], [0, 1], 3, [[], [[2], [1]]], 1) [[], [[2], [1, 3]]] sage: insertion_tableau([[1, 1], []], [2], 1, [[], []], 2) [[], [[1], [0]]] sage: insertion_tableau([[2], []], [2, 0], 1, [[], []], 2) [[], [[1, 0]]] sage: insertion_tableau([[2, 2], []], [0, 2], 2, [[], [[1], [0]]], 2) [[], [[1, 2], [0, 0]]] sage: insertion_tableau([[2, 2], []], [2, 0], 2, [[], [[1, 0]]], 2) [[], [[2, 0], [1, 0]]] sage: insertion_tableau([[2, 2], [1]], [3, 0], 1, [[], []], 3) [[1], [[1, 0], [0]]] """ psave = partition.Partition(skp[1]) partc = skp[1] + [0] * (len(skp[0]) - len(skp[1])) tableau = skew_tableau.SkewTableau(expr=tableau).to_expr()[1] for k in range(len(tableau)): tableau[-(k + 1)] += [0] * (skp[0][k] - partc[k] - len(tableau[-(k + 1)])) ## We construct a tableau from the southwest corner to the northeast one tableau = [[0] * (skp[0][k] - partc[k]) for k in reversed(range(len(tableau), len(skp[0])))] + tableau tableau = skew_tableau.from_expr([skp[1], tableau]).conjugate() tableau = tableau.to_expr()[1] skp = skew_partition.SkewPartition(skp).conjugate().to_list() skp[1].extend([0] * (len(skp[0]) - len(skp[1]))) if len(perm) > len(skp[0]): return None for k in range(len(perm)): if perm[-(k + 1)] != 0: tableau[len(tableau) - len(perm) + k][ skp[0][len(perm) - (k + 1)] - skp[1][len(perm) - (k + 1)] - 1 ] = evaluation return skew_tableau.SkewTableau(expr=[psave.conjugate(), tableau]).conjugate().to_expr()