In this paper, some properties of the image of the geometric lattice of a graphic matroid under a strong map are discussed, and a negative answer to the related open question of Welsh’s book is given.
In 2010,Gábor Czédli and E.Tamás Schmidt mentioned that the best cover-preserving embedding of a given semimodular lattice is not known yet[A cover-preserving embedding of semimodular lattices into geom...In 2010,Gábor Czédli and E.Tamás Schmidt mentioned that the best cover-preserving embedding of a given semimodular lattice is not known yet[A cover-preserving embedding of semimodular lattices into geometric lattices.Advances in Mathematics,225,2455-2463(2010)].That is to say:What are the geometric lattices G such that a given finite semimodular lattice L has a cover-preserving embedding into G with the smallest|G|?In this paper,we propose an algorithm to calculate all the best extending cover-preserving geometric lattices G of a given semimodular lattice L and prove that the length and the number of atoms of every best extending cover-preserving geometric lattice G equal the length of L and the number of non-zero join-irreducible elements of L,respectively.Therefore,we solve the problem on the best cover-preserving embedding of a given semimodular lattice raised by Gábor Czédli and E.Tamás Schmidt.展开更多
The geometric theory of quasicrystal structure is an important subject in quasicrystal research. The authors deduce the quasicrystal plane geometric lattices from the stereograms of quasicrystal space geometric lattic...The geometric theory of quasicrystal structure is an important subject in quasicrystal research. The authors deduce the quasicrystal plane geometric lattices from the stereograms of quasicrystal space geometric lattice , and put them together to form the geometric lattices of quasicrystal structures . The general characteristics of quasicrystal geometric lattices , the relation between structural models and geometric lattices , and the relation formula (k=0 , 2 , 4 , 6 , 8, 10,12) of the symmetric axis between quasicrystal and crystal are discussed based on the quasicrystal space geometric lattices. This is of significant in quasicrystal research .展开更多
基金Foundation item:The NSF(99SL02)of Shaanxi Province and the SF(20609)of China for Postdoctoral Fellow.
文摘In this paper, some properties of the image of the geometric lattice of a graphic matroid under a strong map are discussed, and a negative answer to the related open question of Welsh’s book is given.
基金Supported by the National Natural Science Foundation of China(Grant Nos.11901064 and 12071325)。
文摘In 2010,Gábor Czédli and E.Tamás Schmidt mentioned that the best cover-preserving embedding of a given semimodular lattice is not known yet[A cover-preserving embedding of semimodular lattices into geometric lattices.Advances in Mathematics,225,2455-2463(2010)].That is to say:What are the geometric lattices G such that a given finite semimodular lattice L has a cover-preserving embedding into G with the smallest|G|?In this paper,we propose an algorithm to calculate all the best extending cover-preserving geometric lattices G of a given semimodular lattice L and prove that the length and the number of atoms of every best extending cover-preserving geometric lattice G equal the length of L and the number of non-zero join-irreducible elements of L,respectively.Therefore,we solve the problem on the best cover-preserving embedding of a given semimodular lattice raised by Gábor Czédli and E.Tamás Schmidt.
文摘The geometric theory of quasicrystal structure is an important subject in quasicrystal research. The authors deduce the quasicrystal plane geometric lattices from the stereograms of quasicrystal space geometric lattice , and put them together to form the geometric lattices of quasicrystal structures . The general characteristics of quasicrystal geometric lattices , the relation between structural models and geometric lattices , and the relation formula (k=0 , 2 , 4 , 6 , 8, 10,12) of the symmetric axis between quasicrystal and crystal are discussed based on the quasicrystal space geometric lattices. This is of significant in quasicrystal research .
