伪正则型最大散布线性集与 Segre 簇 ${\cal S}_{n,n}$
组合数学
2013-06-27 v2
摘要
本文研究了一类秩为 的散布 --线性集，位于射影空间 中（，），称为{\it 伪正则型}，推广了 [G. Marino, O. Polverino, R. Trombetti: On --linear sets of and semifields, {\em J. Combin. Theory Ser. A}, {\bf 114} (2007), 769--788] 和 [M. Lavrauw, G. Van de Voorde: Scattered linear sets and pseudoreguli, preprint] 中包含的结果。作为应用，我们利用相关的线性集刻画了几类经典的半域 (semifields)：广义扭曲域 (Generalized Twisted Fields) 和二维 Knuth 半域。
引用
@article{arxiv.1211.3604,
title = {Maximum scattered linear sets of pseudoregulus type and the Segre Variety ${\cal S}_{n,n}$},
author = {G. Lunardon and G. Marino and O. Polverino and R. Trombetti},
journal= {arXiv preprint arXiv:1211.3604},
year = {2013}
}
备注
We have modified Section 4 of the previous version because there was a mistake in Theorem 4.6