In the last few years my interest turned to higher dimensional (not planar) semimodular lattices.
(This research is inspired by some papers of George Grätzer and E. Knapp on planar semimodular lattices,
published in the Acta Sci. Math. Szeged around 2007) pdf
The new results can be considered as a geometric approach. I published another 7 papers with Gábor Czédli, the first of these is
G. Czédli and E. T. Schmidt, How can we derive semilmoduar lattices from distributive lattices?
Acta Math. Acad. Sci. Hungar. 121(2008), 277-282 ( pdf )
is for arbitrary semimodular lattices the another joint papers consider planar lattices.
The main structure theorem of 2D semimodular lattices is in the following paper:
G. Czédli and E. T. Schmidt, Slim semimodular lattices. II.
A description by patchwork systems, Order, 30 (2013), 689-721. ( pdf)
My conjecture: every semimodular lattice is the patchwork of patch lattices.
(New version: January 2016)A structure theorem of semimodular lattices and the Rubik's cube, submitted t AU
pdf figures and tex
Not published results, (sketches):
124. A characterisation of the sources in semimodular lattice ( 2012, renewed: January 2016) pdf
125. A new look at the semimodular lattices, a geometric approach; (2011, under rewriting 2016) pdf
126. Diamond-free 3-dimensional semimodular lattices, (2011, 2012) pdf
127. Rectangular hulls of semimodular lattices, (2011) pdf
128. An extension theorem for finite semimodular lattices, (2014, renewed: January 2016)
129. Semimodular lattices, Slide show , (2012) pdf
132. Rectangular lattices as geometric shapes, (2013) pdf
133. Congruences of 2-dimensional semimodular lattices , (2014),
Slide show: Semimodular lattices, ppt
A 2-dimensional patchwork, htm, gif
A 3-dimensional patchwork, htm, gif
The patch lattice (pigeonhole) gif
The zip gif
Patchwork in the everyday life: pieces of cloth of various colors and shape sewn together
28 January 2016