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Irreducible subcube partitions

Title data

Filmus, Yuval ; Hirsch, Edward A. ; Ihringer, Ferdinand ; Kurz, Sascha ; Ryazanov, Artur ; Smal, Alexander V. ; Vinyals, Marc:
Irreducible subcube partitions.
Event: Annual Meeting of the IMU , 03.09.2023 , Rehovot, Israel.
(Conference item: Conference , Speech )

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 sub-partitions 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,...,q-1}^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: Conference item (Speech)
Refereed: No
Additional notes: speaker: Yuval Filmus
Keywords: hitting formulas; partitions; hypercubes; Boolean
Subject classification: Mathematics Subject Classification Code: 05D05 (05D99 51E23)
Institutions of the University: Faculties > Faculty of Mathematics, Physics und Computer Science
Faculties > Faculty of Mathematics, Physics und Computer Science > Department of Mathematics > Chair Mathematical Economics
Result of work at the UBT: Yes
DDC Subjects: 000 Computer Science, information, general works > 004 Computer science
500 Science > 510 Mathematics
Date Deposited: 13 Sep 2023 07:29
Last Modified: 13 Sep 2023 07:29