Journal of Combinatorial Theory Series A ( IF 1.1 ) Pub Date : 2020-12-15 , DOI: 10.1016/j.jcta.2020.105386 Daniele Bartoli , Maria Montanucci
Let be a q-polynomial. If the -subspace defines a maximum scattered linear set, then we call a scattered polynomial of index t. The asymptotic behavior of scattered polynomials of index t is an interesting open problem. In this sense, exceptional scattered polynomials of index t are those for which U is a maximum scattered linear set in for infinitely many m. The classifications of exceptional scattered monic polynomials of index 0 (for ) and of index 1 were obtained in [1]. In this paper we complete the classifications of exceptional scattered monic polynomials of index 0 for . Also, some partial classifications are obtained for arbitrary t. As a consequence, the classification of exceptional scattered monic polynomials of index 2 is given.
中文翻译:
关于特殊分散多项式的分类
让 是q多项式。如果-子空间 定义一个最大的分散线性集,然后我们称 索引为t的分散多项式。指数为t的分散多项式的渐近行为是一个有趣的开放问题。从这个意义上讲,索引为t的特殊分散多项式是那些U是无限数m。指数为0的异常零散单项多项式的分类)和索引1在[1]中获得。在本文中,我们完成了索引为0的异常零散单项多项式的分类。同样,对于任意t,可以获得一些部分分类。结果,给出了索引为2的异常分散单项多项式的分类。