An Identity of Distributive Lattices

2014/02/25 by Mukherjee, Himadri
#Combinatorics (math.CO) #FOS: Mathematics

paper · doi:10.48550/arxiv.1402.6146

Abstract

In a finite distributive lattice Ł we define two functions s(α)=|\δ∈ L | δ≤ α\| and l(α)=|\δ∈ L | δ≥ α\|. In this present article we prove that the sum of these two functions over a finite distributive lattice are equal. Using this identity we give a formula for the number of non-comparable pairs of elements in a finite distributive lattice.

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