Height and semimodularity in finite 0,1-posets
Let P be a finite poset with 0 and 1. \(a\vee b\) is a freely chosen minimal upper bound of a and b. \(a\wedge b\) is defined dually. (L;\(\vee,\wedge)\) is called a \(\chi\)-lattice derived from P. h(a) denotes the length of a longest maximal chain between 0 and a. A concept of semimodularity is defined so that \(h(a)+h(b)\geq h(a\vee b)+h(a\wedge b)\) holds in any \(\chi\)-lattice derived from P.
scientific article; zbMATH DE number 4023344