Topology and Combinatorics of Partitions of Masses by Hyperplanes
| dc.creator | Mani-Levitska, Peter | |
| dc.creator | Vrecica, Sinisa | |
| dc.creator | Zivaljevic, Rade | |
| dc.date | 2003-10-23 | |
| dc.date.accessioned | 2026-07-07T05:02:12Z | |
| dc.date.available | 2026-07-07T05:02:12Z | |
| dc.description | One of our result is that 5 measurable sets in $R^8$ always admit an equipartition by 2 hyperplanes. This is an instance of a general equipartition problem (formulated by B. Gr{\" u}nbaum and H. Hadwiger) which can be reduced to the question of (non)existence of a $W_k$-equivariant map where $W_k$ is the group of symmetries of a $k$-cube. We show that the computation of relevant cohomology/bordism obstruction classes often reduces to the question of enumerating the classes of immersed curves in $\mathbb{R}^2$ with a prescribed type and number of intersections with the coordinate axes, which in turn leads to a problem of enumerating classes of cyclic signed $AB$-words. | |
| dc.description | 27 pages, 7 figures | |
| dc.identifier | https://arxiv.org/abs/math/0310377 | |
| dc.identifier | http://arxiv.org/abs/math/0310377 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/68967 | |
| dc.subject | Combinatorics | |
| dc.subject | Algebraic Topology | |
| dc.subject | 05A15, 51M20, 52B45, 55N25, 55S35, 57R25 | |
| dc.title | Topology and Combinatorics of Partitions of Masses by Hyperplanes | |
| dc.type | text |