Presented By: Learning Seminar in Algebraic Combinatorics - Department of Mathematics
Learning Seminar in Algebraic Combinatorics: Projective system of posets from set partitions
Amrita Acharyya
It is known when we call a poset P, a P-chain permutational poset, given a subset of permutations
P of the symmetric group S_n. 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. 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.
P of the symmetric group S_n. 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. 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.
Co-Sponsored By
Explore Similar Events
-
Loading Similar Events...
