Join-irreducible Boolean functions
| dc.creator | Bouaziz, Moncef | |
| dc.creator | Couceiro, Miguel | |
| dc.creator | Pouzet, Maurice | |
| dc.date | 2009-03-23 | |
| dc.date.accessioned | 2026-07-07T12:55:41Z | |
| dc.date.available | 2026-07-07T12:55:41Z | |
| dc.description | This paper is a contribution to the study of a quasi-order on the set $Ω$ of Boolean functions, the \emph{simple minor} quasi-order. We look at the join-irreducible members of the resulting poset $\tildeΩ$. Using a two-way correspondence between Boolean functions and hypergraphs, join-irreducibility translates into a combinatorial property of hypergraphs. We observe that among Steiner systems, those which yield join-irreducible members of $\tildeΩ$ are the -2-monomorphic Steiner systems. We also describe the graphs which correspond to join-irreducible members of $\tildeΩ$. | |
| dc.description | The current manuscript constitutes an extension to the paper "Irreducible Boolean Functions" (arXiv:0801.2939v1) | |
| dc.identifier | https://arxiv.org/abs/0903.3848 | |
| dc.identifier | http://arxiv.org/abs/0903.3848 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/224335 | |
| dc.subject | Combinatorics | |
| dc.subject | 05C75, 05C65, 05B05, 05B07, 06A07, 06E30, 94C10 | |
| dc.title | Join-irreducible Boolean functions | |
| dc.type | text |