caa a22 4500 475777980 CHVBK 20180406123636.0 cr unu---uuuuu 170329e20000301xx s 000 0 eng 10.1007/s003730050001 doi (NATIONALLICENCE)springer-10.1007/s003730050001 Lower Semimodular Types of Lattices: Frankl's Conjecture Holds for Lower Quasi-Semimodular Lattices [Elektronische Daten] [Tetsuya Abe, Bumpei Nakano] Abstract.: We introduce a measure of how far a lattice L is from being lower semimodular. We call it the lower semimodular type of L. A lattice has lower semimodular type zero if and only if it is lower semimodular. In this paper we discuss properties of the measure and we show that Frankl's conjecture holds for lower quasi-semimodular lattices: if a lattice L is lower quasi-semimodular then there is a join-irreducible element x in L such that the size of the principal filter generated by x is at most (|L|− 1) /2. Springer-Verlag Tokyo, 2000 Abe Tetsuya Department of Systems Science, Tokyo Institute of Technology 4259 Nagatsuta, Midori-ku, Yokohama 226-8502, Japan. e-mail: abe@iaws−20.ia.noda.sut.ac.jp, JP aut Nakano Bumpei Department of Artificial Intelligence and Systems Science, Tokyo Institute of Technology, 4259, Nagatsuta, Midori-ku, Yokohama 226-8502, Japan e-mail: bnakano@nkn.dis.titech.ac.jp, JP aut https://doi.org/10.1007/s003730050001 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1007/s003730050001 text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Abe Tetsuya Department of Systems Science, Tokyo Institute of Technology 4259 Nagatsuta, Midori-ku, Yokohama 226-8502, Japan. e-mail: abe@iaws−20.ia.noda.sut.ac.jp, JP aut NATIONALLICENCE 700 1- Nakano Bumpei Department of Artificial Intelligence and Systems Science, Tokyo Institute of Technology, 4259, Nagatsuta, Midori-ku, Yokohama 226-8502, Japan e-mail: bnakano@nkn.dis.titech.ac.jp, JP aut Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer