The distinguishing number of the direct product and wreath product action
| dc.creator | Chan, Melody | |
| dc.date | 2006-01-17 | |
| dc.date.accessioned | 2026-07-07T06:59:01Z | |
| dc.date.available | 2026-07-07T06:59:01Z | |
| dc.description | Let G be a group acting faithfully on a set X. The distinguishing number of the action of G on X is the smallest number of colors such that there exists a coloring of X where no nontrivial group element induces a color-preserving permutation of X. In this paper, we consider the distinguishing number of two important product actions, the wreath product and the direct product. Given groups G and H acting on sets X and Y respectively, we characterize the distinguishing number of the wreath product of G and H in terms of the number of distinguishing colorings of X with respect to G and the distinguishing number of the action of H on Y. We also prove a recursive formula for the distinguishing number of the action of the Cartesian product of two symmetric groups S_m x S_n on [m] x [n]. | |
| dc.description | 16 pages, to appear in the Journal of Algebraic Combinatorics | |
| dc.identifier | https://arxiv.org/abs/math/0601414 | |
| dc.identifier | http://arxiv.org/abs/math/0601414 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/107592 | |
| dc.subject | Combinatorics | |
| dc.subject | Group Theory | |
| dc.subject | 05E15 (Primary) 20B25, 20D60 (Secondary) | |
| dc.title | The distinguishing number of the direct product and wreath product action | |
| dc.type | text |