Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
5777540 | Journal of Combinatorial Theory, Series A | 2017 | 25 Pages |
Abstract
We give a closed formula for the number of partitions λ of n such that the corresponding irreducible representation Vλ of Sn has non-trivial determinant. We determine how many of these partitions are self-conjugate and how many are hooks. This is achieved by characterizing the 2-core towers of such partitions. We also obtain a formula for the number of partitions of n such that the associated permutation representation of Sn has non-trivial determinant.
Related Topics
Physical Sciences and Engineering
Mathematics
Discrete Mathematics and Combinatorics
Authors
Arvind Ayyer, Amritanshu Prasad, Steven Spallone,