@article {
author = {Babaei, Esmaeil and Zamani, Yousef},
title = {Symmetry classes of polynomials associated with the direct product of permutation groups},
journal = {International Journal of Group Theory},
volume = {3},
number = {4},
pages = {63-69},
year = {2014},
publisher = {University of Isfahan},
issn = {2251-7650},
eissn = {2251-7669},
doi = {10.22108/ijgt.2014.5479},
abstract = {Let $G_{i} $ be a subgroup of $ S_{m_{i}} ,\ 1 \leq i \leq k$. Suppose $\chi_{i}$ is an irreducible complex character of $G_{i}$. We consider $ G_{1}\times \cdots \times G_{k} $ as subgroup of $ S_{m} $, where $ m=m_{1}+\cdots +m_{k} $. In this paper, we give a formula for the dimension of $H_{d}(G_{1}\times \cdots \times G_{k}, \chi_{1}\times\cdots \times \chi_{k})$ and investigate the existence of an o-basis of this type of classes.},
keywords = {Symmetric polynomials,symmetry class of polynomials,orthogonal basis,permutaion groups,complex characters},
url = {https://ijgt.ui.ac.ir/article_5479.html},
eprint = {https://ijgt.ui.ac.ir/article_5479_0495fb15f251988634840c9c7812f01e.pdf}
}