Criteria for Balance in Abelian Gain Graphs with Applications to Geometry
نویسندگان
چکیده
Consider a gain graph with abelian gain group having no odd torsion. If there is a binary cycle basis each of whose members can be lifted to a closed walk whose gain is the identity, then the gain graph is balanced, provided that the graph is finite or the group has no nontrivial infinitely 2-divisible elements.
منابع مشابه
Criteria for Balance in Abelian Gain Graphs, with Applications to Piecewise-Linear Geometry
Consider a gain graph with abelian gain group having no odd torsion. If there is a basis of the graph’s binary cycle space each of whose members can be lifted to a closed walk whose gain is the identity, then the gain graph is balanced, provided that the graph is finite or the group has no nontrivial infinitely 2-divisible elements. We apply this theorem to deduce a result on the projective geo...
متن کاملCriteria for Balance in Abelian Gain Graphs, with an Application to Piecewise-Linear Geometry
Consider a gain graph with abelian gain group having no odd torsion. If there is a basis of the graph’s binary cycle space each of whose members can be lifted to a closed walk whose gain is the identity, then the gain graph is balanced, provided that the graph is finite or the group has no nontrivial infinitely 2-divisible elements. We apply this theorem to deduce a result on the structural geo...
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تاریخ انتشار 2008