We study a new set of duality relations between weighted,combinatoric invariants of a graph G.The dualities arise from a non-linear transform B,acting on the weight function p.We define B on a space of real-valued fun...We study a new set of duality relations between weighted,combinatoric invariants of a graph G.The dualities arise from a non-linear transform B,acting on the weight function p.We define B on a space of real-valued functions O and investigate its properties.We show that three invariants(the weighted independence number,the weighted Lovasz number,and the weighted fractional packing number)are fixed points of B^2,but the weighted Shannon capacity is not.We interpret these invariants in the study of quantum non-locality.展开更多
This paper introduces three kinds of operators on planar graphs with binary weights on edges, for which combinatorial invariants on two kinds of equivalences are found. Further, it is shown that the Jones polynomial a...This paper introduces three kinds of operators on planar graphs with binary weights on edges, for which combinatorial invariants on two kinds of equivalences are found. Further, it is shown that the Jones polynomial and the bracket polynomial which are proved to be new topological invariants on knots in topology become special cases. Moreover, these invariants are a kind of generalization of Tutte polynomial on graphs.展开更多
基金supported by the Templeton Religion Trust(Grant No.TRT 0159)supported by USA Army Research Office(ARO)(Grant No.W911NF1910302)。
文摘We study a new set of duality relations between weighted,combinatoric invariants of a graph G.The dualities arise from a non-linear transform B,acting on the weight function p.We define B on a space of real-valued functions O and investigate its properties.We show that three invariants(the weighted independence number,the weighted Lovasz number,and the weighted fractional packing number)are fixed points of B^2,but the weighted Shannon capacity is not.We interpret these invariants in the study of quantum non-locality.
文摘This paper introduces three kinds of operators on planar graphs with binary weights on edges, for which combinatorial invariants on two kinds of equivalences are found. Further, it is shown that the Jones polynomial and the bracket polynomial which are proved to be new topological invariants on knots in topology become special cases. Moreover, these invariants are a kind of generalization of Tutte polynomial on graphs.
