Journal of Combinatorial Theory Series A ( IF 0.9 ) Pub Date : 2021-09-02 , DOI: 10.1016/j.jcta.2021.105535 Marino Romero 1
In the context of the (generalized) Delta Conjecture and its compositional form, D'Adderio, Iraci, and Vanden Wyngaerd recently stated a conjecture relating two symmetric function operators, and . We prove this Theta Operator Conjecture, finding it as a consequence of the five-term relation of Mellit and Garsia. As a result, we find surprising ways of writing the operators. Even though we deal specifically with the relation between the and operators, our work introduces a method for finding relations between and other plethystic operators which are important in this area of study.
中文翻译:
θ 算子猜想的证明
在(广义)Delta 猜想及其组合形式的上下文中,D'Adderio、Iraci 和 Vanden Wyngaerd 最近陈述了一个关于两个对称函数算子的猜想, 和 . 我们证明了这个 Theta 算子猜想,发现它是 Mellit 和 Garsia 的五项关系的结果。结果,我们发现了令人惊讶的书写方式运营商。尽管我们专门处理了两者之间的关系 和 运算符,我们的工作介绍了一种查找之间关系的方法 和其他在这个研究领域很重要的 plethystic 算子。