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The Best Extending Cover-preserving Geometric Lattices of Semimodular Lattices.
- Source :
-
Acta Mathematica Sinica . Jul2023, Vol. 39 Issue 7, p1369-1388. 20p. - Publication Year :
- 2023
-
Abstract
- 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. [ABSTRACT FROM AUTHOR]
- Subjects :
- *PROBLEM solving
*MATHEMATICS
*ATOMS
Subjects
Details
- Language :
- English
- ISSN :
- 14398516
- Volume :
- 39
- Issue :
- 7
- Database :
- Academic Search Index
- Journal :
- Acta Mathematica Sinica
- Publication Type :
- Academic Journal
- Accession number :
- 171806125
- Full Text :
- https://doi.org/10.1007/s10114-023-1531-1