Title data
Filmus, Yuval ; Hirsch, Edward ; Ihringer, Ferdinand ; Kurz, Sascha ; Riazanov, Artur ; Smal, Alexander ; Vinyals, Marc:
Irreducible Subcube Partitions.
Bayreuth
,
2023
.  38 p.
DOI: https://doi.org/10.15495/EPub_UBT_00006837
This is the latest version of this item.
Abstract in another language
A subcube partition is a partition of the Boolean cube {0,1}^n into subcubes. A subcube partition is irreducible if the only subpartitions whose union is a subcube are singletons and the entire partition. A subcube partition is tight if it "mentions" all coordinates.
We study extremal properties of tight irreducible subcube partitions: minimal size, minimal weight, maximal number of points, maximal size, and maximal minimum dimension.
We also consider the existence of homogeneous tight irreducible subcube partitions, in which all subcubes have the same dimensions. We additionally study subcube partitions of {0,...,q1}^n, and partitions of GF(2)^n into affine subspaces, in both cases focusing on the minimal size.
Our constructions and computer experiments lead to several conjectures on the extremal values of the aforementioned properties.
Further data
Item Type:  Preprint, postprint 

Keywords:  hitting formulas; partitions; hypercubes; Boolean 
Institutions of the University:  Faculties > Faculty of Mathematics, Physics und Computer Science Faculties > Faculty of Mathematics, Physics und Computer Science > Department of Mathematics Faculties > Faculty of Mathematics, Physics und Computer Science > Department of Mathematics > Chair Mathematical Economics Faculties 
Result of work at the UBT:  Yes 
DDC Subjects:  000 Computer Science, information, general works > 004 Computer science 500 Science > 510 Mathematics 
Date Deposited:  26 Jan 2023 07:09 
Last Modified:  26 Jan 2023 07:09 
URI:  https://eref.unibayreuth.de/id/eprint/73528 
Available Versions of this Item

Irreducible Subcube Partitions. (deposited 23 Jan 2023 14:31)
 Irreducible Subcube Partitions. (deposited 26 Jan 2023 07:09) [Currently Displayed]