Solving General Lattice Puzzles

Author(s):  
Gill Barequet ◽  
Shahar Tal
Keyword(s):  



1960 ◽  
Vol 12 ◽  
pp. 582-591 ◽  
Author(s):  
D. T. Finkbeiner

The study of structural or arithmetic properties of a general lattice often can be facilitated by imbedding as a sublattice of a lattice of a more restricted type whose properties are known. However, if is too restricted, a general imbedding is impossible; for example, cannot be modular because , as a sublattice of , would then have to be modular. One of the best results of this nature has been given by Dilworth in an unpublished work in which he shows that any finite dimensional lattice is isomorphic to a sublattice of a semi-modular point lattice (1, pp. 105 and 110). In the present paper Dilworth's imbedding process is modified to obtain a sharper result: Any finite dimensional lattice is isometrically isomorphic to a sublattice of a semi-modular lattice which has the same number of points as and which preserves basic properties of the join-irreducible arithmetic of .



2020 ◽  
Vol 282 (3) ◽  
pp. 1185-1199 ◽  
Author(s):  
Anna Maria Gambaro ◽  
Ioannis Kyriakou ◽  
Gianluca Fusai


1989 ◽  
Vol 46 (1) ◽  
pp. 512-517
Author(s):  
I. A. Ignatyuk


1975 ◽  
Vol 31 (2) ◽  
pp. 369-372 ◽  
Author(s):  
H.D.B. Jenkins ◽  
T.C. Waddington






1997 ◽  
Vol 55 (4) ◽  
pp. 2122-2143 ◽  
Author(s):  
Gökhan Esirgen ◽  
N. E. Bickers


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