Minimal Bar Tableaux
| dc.creator | Clifford, Peter | |
| dc.date | 2003-11-24 | |
| dc.date.accessioned | 2026-07-07T05:03:12Z | |
| dc.date.available | 2026-07-07T05:03:12Z | |
| dc.description | Motivated by Stanley's results in \cite{St02}, we generalize the rank of a partition $λ$ to the rank of a shifted partition $S(λ)$. We show that the number of bars required in a minimal bar tableau of $S(λ)$ is max$(o, e + (\ell(λ) \mathrm{mod} 2))$, where $o$ and $e$ are the number of odd and even rows of $λ$. As a consequence we show that the irreducible projective characters of $S_n$ vanish on certain conjugacy classes. Another corollary is a lower bound on the degree of the terms in the expansion of Schur's $Q_λ$ symmetric functions in terms of the power sum symmetric functions. | |
| dc.description | 12 pages, 7 figures | |
| dc.identifier | https://arxiv.org/abs/math/0311418 | |
| dc.identifier | http://arxiv.org/abs/math/0311418 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/69321 | |
| dc.subject | Combinatorics | |
| dc.subject | 05E05, 05E10, 20C25, 20C30 | |
| dc.title | Minimal Bar Tableaux | |
| dc.type | text |