TY - JOUR
ID - 85730
TI - Frankl's Conjecture for a subclass of semimodular lattices
JO - Categories and General Algebraic Structures with Applications
JA - CGASA
LA - en
SN - 2345-5853
AU - Joshi, Vinayak
AU - Waphare, Baloo
AD - Department of Mathematics, Savitribai Phule Pune University (Formerly, University of Pune) Ganeshkhind Road, Pune - 411007
AD - Department of Mathematics, Savitribai Phule Pune University,
Pune-411007, India.
Y1 - 2019
PY - 2019
VL - 11
IS - Special Issue Dedicated to Prof. George A. Grätzer
SP - 197
EP - 206
KW - Union-Closed Sets Conjecture
KW - Frankl's Conjecture
KW - semimodular lattice
KW - adjunct operation
DO - 10.29252/cgasa.11.1.197
N2 - In this paper, we prove Frankl's Conjecture for an upper semimodular lattice $L$ such that $|J(L)setminus A(L)| leq 3$, where $J(L)$ and $A(L)$ are the set of join-irreducible elements and the set of atoms respectively. It is known that the class of planar lattices is contained in the class of dismantlable lattices and the class of dismantlable lattices is contained in the class of lattices having breadth at most two. We provide a very short proof of the Conjecture for the class of lattices having breadth at most two. This generalizes the results of Joshi, Waphare and Kavishwar as well as Czédli and Schmidt.
UR - https://cgasa.sbu.ac.ir/article_85730.html
L1 - https://cgasa.sbu.ac.ir/article_85730_335445da865e1a5e147830cee5b78a6e.pdf
ER -