Analyzing Subuniverse Counts in Finite Semilattices: Unveiling the Rankings and Descriptions

2024/08/18 by Ahmed, Delbrin, Salih, Muwafaq, Haje, Dilbak
#Combinatorics (math.CO) #FOS: Mathematics

paper · doi:10.48550/arxiv.2408.09595

Abstract

Let (L,\vee) be a finite n-element semilattice where n≥ 5. We prove that the fourth largest number of subuniverses of an n-element semilattice is 25⋅ 2^n-5, the fifth largest number is 24.5⋅ 2^n-5, and the sixth one is 24⋅ 2^n-5. Also, we describe the n-element semilattices with exactly 25⋅ 2^n-5, 24.5⋅ 2^n-5 or 24⋅ 2^n-5 subuniverses.

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