def _to_m(self, part): r""" Returns a function which gives the coefficient of part2 in the monomial expansion of self(part). INPUT: - ``self`` -- an instance of the LLT hcospin basis - ``part`` -- a partition OUTPUT: - returns a function which accepts a partition and returns the coefficient in the expansion of the monomial basis EXAMPLES:: sage: HCosp3 = SymmetricFunctions(FractionField(QQ['t'])).llt(3).hcospin() sage: f21 = HCosp3._to_m(Partition([2,1])) sage: [f21(p) for p in Partitions(3)] [1, t + 1, 2*t + 1] sage: HCosp3.symmetric_function_ring().m()( HCosp3[2,1] ) (2*t+1)*m[1, 1, 1] + (t+1)*m[2, 1] + m[3] """ level = self.level() f = lambda part2: QQt(ribbon_tableau.cospin_polynomial([level*i for i in part], part2, level)) return f
def _to_m(self, part): """ Returns a function which gives the coefficient of part2 in the monomial expansion of self(part). EXAMPLES:: sage: from sage.combinat.sf.llt import * sage: HCosp3 = LLT_cospin(QQ, 3) sage: f21 = HCosp3._to_m(Partition([2,1])) sage: [f21(p) for p in Partitions(3)] [1, t + 1, 2*t + 1] """ BR = self.base_ring() level = self.level() f = lambda part2: BR(ribbon_tableau.cospin_polynomial([level*i for i in part], part2, level)) return f
def _to_m(self, part): """ Returns a function which gives the coefficient of part2 in the monomial expansion of self(part). EXAMPLES:: sage: from sage.combinat.sf.llt import * sage: HCosp3 = LLT_cospin(QQ, 3) sage: f21 = HCosp3._to_m(Partition([2,1])) sage: [f21(p) for p in Partitions(3)] [1, t + 1, 2*t + 1] """ BR = self.base_ring() level = self.level() f = lambda part2: BR( ribbon_tableau.cospin_polynomial([level * i for i in part], part2, level)) return f