1,151,609 research outputs found
Submatrices of character tables and basic sets
In this investigation of character tables of finite groups we study basic
sets and associated representation theoretic data for complementary sets of
conjugacy classes. For the symmetric groups we find unexpected properties of
characters on restricted sets of conjugacy classes, like beautiful
combinatorial determinant formulae for submatrices of the character table and
Cartan matrices with respect to basic sets; we observe that similar phenomena
occur for the transition matrices between power sum symmetric functions to
bounded partitions and the -Schur functions introduced by Lapointe and
Morse. Arithmetic properties of the numbers occurring in this context are
studied via generating functions.Comment: 18 pages; examples added, typos removed, some further minor changes,
references update
Intersection sets, three-character multisets and associated codes
In this article we construct new minimal intersection sets in
sporting three intersection numbers with hyperplanes; we
then use these sets to obtain linear error correcting codes with few weights,
whose weight enumerator we also determine. Furthermore, we provide a new family
of three-character multisets in with even and we
also compute their weight distribution.Comment: 17 Pages; revised and corrected result
Character Degrees of Normally Monomial Maximal Class 5-Groups
This paper will impose limits on the possible sets of irreducible character degrees of a normally monomial 5-group of maximal class
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