Paper
Inverse limits of various posets
Authors
Amrita Acharyya
Abstract
It is known when we call a poset P, a -chain permutational poset, given a subset of permutations of the symmetric group . In this work, we use the same idea to study subsets of words of length , 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 . Varying only, and also varying and (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 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 -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.