Counting formulas for glued lattices

✍ Scribed by Klaus Reuter

• Book ID: 104748860
• Publisher: Springer Netherlands
• Year: 1985
• Tongue: English
• Weight: 438 KB
• Volume: 1
• Category: Article
• ISSN: 0167-8094
• DOI: 10.1007/bf00383603

✦ Synopsis

A tolerance relation 0 of a lattice L, i.e., a reflexive and symmetric relation of L which is compatible with join and meet, is called glued if covering blocks of 0 have nonempty intersection. For a lattice L with a glued tolerance relation we prove a formula counting the number of elements of L with exactly k lower (upper) covers. Moreover, we prove similar formulas for incidence structures and graphs and we give a new proof of Dilworth's covering theorem.

AMS (MOS) subject classifications (1980). 05A15, 06B05