Two by two squares in set partitions

Year, pages: 2020, 29 - 40

A partition $π$ of a set $S$ is a collection $B₁, B₂,…, B_k$ of non-empty disjoint subsets, called blocks, of $S$ such that $\bigcup _i=1^kB_i=S$. We assume that $B₁, B₂,…, B_k$ are listed in canonical order; that is in increasing order of their minimal elements; so $\min B₁<\min B₂<… < \min B_k$. A partition into $k$ blocks can be represented by a word $π=π₁π₂…π_n$, where for $1 ≤ j ≤ n$, $π_j \in [k]$ and $\bigcup _i=1ⁿ \{π_i\}=[k]$, and $π_j$ indicates that $j \in B_πj$. The canonical representations of all set partitions of $[n]$ are precisely the words $π=π₁π₂…π_n$ such that $π₁=1$, and if $i

How to cite:

ISO 690:

Archibald, M., Blecher, A., Brennan, C., Knopfmacher, A., Mansour, T. 2020. Two by two squares in set partitions. In Mathematica Slovaca, vol. 70, no.1, pp. 29-40. 0139-9918. DOI: https://doi.org/10.1515/ms-2017-0328

APA:

Archibald, M., Blecher, A., Brennan, C., Knopfmacher, A., Mansour, T. (2020). Two by two squares in set partitions. Mathematica Slovaca, 70(1), 29-40. 0139-9918. DOI: https://doi.org/10.1515/ms-2017-0328

About edition:

Publisher: Mathematical Institute, Slovak Academy of Sciences, Bratislava

Published: 13. 1. 2020