2025/12/12 by Amrita Acharyya, Acharyya, Amrita
Mathematics · #Advanced Combinatorial Mathematics #Combinatorics (math.CO) #FOS: Mathematics #Finite Group Theory Research #Limits and Structures in Graph Theory
paper · pdf · doi:10.48550/arxiv.2512.12007
openalex publication_date 2025/12/12 · openalex created_date 2025/12/17 · openalex updated_date 2026/07/28
It is known when we call a poset P, a P-chain permutational poset, given a subset of permutations P of the symmetric group Sn. In this work, we use the same idea to study subsets of words of length n, that are not necessarily permutations, for example: especially when they are certain classes of restricted growth functions induced by set partitions in standard form over [n]=\1,2⋯ n\. Varying n only, and also varying n and k (the number of blocks of the set partitions) simultaneously, we can show that those posets form a projective system of trees and lattices (after giving a lattice structure in a natural way). These poset structures can be extended over signed restricted growth functions for standard type B set partitions over ⟨ n⟩=\-1,-2,⋯ n,0,1,2⋯ n\ as well. We investigate properties of the tree and lattice structures of these projective systems. In this scenario we further bring up some other posets like P-Partition posets of snake graph of continued fractions, Ascent lattices on Dyck Paths, certain type of lattice induced by generalisec fibonnaci number and Stanley order, lattices induced by non-crossing set partitions.