Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Preprint |
| Veröffentlicht: |
2025
|
| Schlagworte: | |
| Online-Zugang: | https://arxiv.org/abs/2512.12007 |
| Tags: |
Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
|
| _version_ | 1866909959402291200 |
|---|---|
| author | Acharyya, Amrita |
| author_facet | Acharyya, Amrita |
| contents | It is known when we call a poset P, a $\mathcal{P}$-chain permutational poset, given a subset of permutations $\mathcal{P}$ 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 $[n]=\{1,2\cdots n\}$. 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 $\langle n\rangle=\{-1,-2,\cdots n,0,1,2\cdots n\}$ 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 $\mathcal{P}$-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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2512_12007 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Inverse limits of various posets Acharyya, Amrita Combinatorics It is known when we call a poset P, a $\mathcal{P}$-chain permutational poset, given a subset of permutations $\mathcal{P}$ 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 $[n]=\{1,2\cdots n\}$. 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 $\langle n\rangle=\{-1,-2,\cdots n,0,1,2\cdots n\}$ 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 $\mathcal{P}$-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. |
| title | Inverse limits of various posets |
| topic | Combinatorics |
| url | https://arxiv.org/abs/2512.12007 |