Geodesic
On a positivity conjecture in the character table of \(S_n\)
Sheila Sundaram1
1Pierrepont School
The electronic journal of combinatorics, Tome 26 (2019) no. 1
Cet article a éte moissonné depuis la source The Electronic Journal of Combinatorics website

Voir la notice de l'article

In previous work of this author it was conjectured that the sum of power sums $p_\lambda,$ for partitions $\lambda$ ranging over an interval $[(1^n), \mu]$ in reverse lexicographic order, is Schur-positive. Here we investigate this conjecture and establish its truth in the following special cases: for $\mu\in [(n-4,1^4), (n)]$ or $\mu\in [(1^n), (3,1^{n-3})], $ or $\mu=(3, 2^k, 1^r)$ when $k\geq 1$ and $0\leq r\leq 2.$ Many new Schur positivity questions are presented.
DOI : 10.37236/8186
Classification : 05E10, 05E18, 05A17, 11P81, 06A07, 20B30, 20C05, 20C15
Mots-clés : Schur positivity, character table, symmetric group

Sheila Sundaram  1

1 Pierrepont School 
@article{10_37236_8186,
     author = {Sheila Sundaram},
     title = {On a positivity conjecture in the character table of {\(S_n\)}},
     journal = {The electronic journal of combinatorics},
     year = {2019},
     volume = {26},
     number = {1},
     doi = {10.37236/8186},
     zbl = {1409.05215},
     url = {http://geodesic.mathdoc.fr/articles/10.37236/8186/}
}
TY  - JOUR
AU  - Sheila Sundaram
TI  - On a positivity conjecture in the character table of \(S_n\)
JO  - The electronic journal of combinatorics
PY  - 2019
VL  - 26
IS  - 1
UR  - http://geodesic.mathdoc.fr/articles/10.37236/8186/
DO  - 10.37236/8186
ID  - 10_37236_8186
ER  - 
%0 Journal Article
%A Sheila Sundaram
%T On a positivity conjecture in the character table of \(S_n\)
%J The electronic journal of combinatorics
%D 2019
%V 26
%N 1
%U http://geodesic.mathdoc.fr/articles/10.37236/8186/
%R 10.37236/8186
%F 10_37236_8186
Sheila Sundaram. On a positivity conjecture in the character table of \(S_n\). The electronic journal of combinatorics, Tome 26 (2019) no. 1. doi: 10.37236/8186

Cité par Sources :