An Identity of Distributive Lattices
Mukherjee, Himadri
Original · EN
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.
English translation
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