The distinguishing number of the direct product and wreath product action

Details The distinguishing number of the direct product and wreath product action The distinguishing number of the direct product and wreath product action

2006-01-17

arxiv.org/abs/math/0601414v1

Mathematics

Combinatorics

16 pages, to appear in the Journal of Algebraic Combinatorics

Scientific paper

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].

Affiliated with

Also associated with

No associations

Rating

The distinguishing number of the direct product and wreath product action does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with The distinguishing number of the direct product and wreath product action, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and The distinguishing number of the direct product and wreath product action will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-229138