The well-known sequentially lifted cover inequality is widely employed in solving mixed integer programs.However,it is still an open question whether a sequentially lifted cover inequality can be computed in polynomia...The well-known sequentially lifted cover inequality is widely employed in solving mixed integer programs.However,it is still an open question whether a sequentially lifted cover inequality can be computed in polynomial time for a given minimal cover(Gu et al.(1999)).We show that this problem is N P-hard,thus giving a negative answer to the question.展开更多
Davis and Januszkiewicz introduced(real and complex) universal complexes to give an equivalent definition of characteristic maps of simple polytopes, which now can be seen as "colorings". The author derives ...Davis and Januszkiewicz introduced(real and complex) universal complexes to give an equivalent definition of characteristic maps of simple polytopes, which now can be seen as "colorings". The author derives an equivalent definition of Buchstaber invariants of a simplicial complex K, then interprets the difference of the real and complex Buchstaber invariants of K as the obstruction to liftings of nondegenerate simplicial maps from K to the real universal complex or the complex universal complex. It was proved by Ayzenberg that real universal complexes can not be nondegenerately mapped into complex universal complexes when dimension is 3. This paper presents that there is a nondegenerate map from 3-dimensional real universal complex to 4-dimensional complex universal complex.展开更多
基金supported by National Natural Science Foundation of China(Grant Nos.11631013 and 11331012)the National Basic Research Program of China(Grant No.2015CB856002)the Major Project to Promote Development of Big Data from National Development and Reform Commission(Grant No.2016-999999-65-01-000696-01)。
文摘The well-known sequentially lifted cover inequality is widely employed in solving mixed integer programs.However,it is still an open question whether a sequentially lifted cover inequality can be computed in polynomial time for a given minimal cover(Gu et al.(1999)).We show that this problem is N P-hard,thus giving a negative answer to the question.
基金supported by the National Natural Science Foundation of China(Nos.11371093,10931005)
文摘Davis and Januszkiewicz introduced(real and complex) universal complexes to give an equivalent definition of characteristic maps of simple polytopes, which now can be seen as "colorings". The author derives an equivalent definition of Buchstaber invariants of a simplicial complex K, then interprets the difference of the real and complex Buchstaber invariants of K as the obstruction to liftings of nondegenerate simplicial maps from K to the real universal complex or the complex universal complex. It was proved by Ayzenberg that real universal complexes can not be nondegenerately mapped into complex universal complexes when dimension is 3. This paper presents that there is a nondegenerate map from 3-dimensional real universal complex to 4-dimensional complex universal complex.
