直和的切片秩
组合数学
2021-08-12 v2
摘要
我们证明两个张量的直和的切片秩等于它们切片秩的和。上界是平凡的，但下界需要不止一行的证明，其原因我们予以解释。该结果推广了 Tao 所证的事实：对角张量的切片秩等于该张量非零项的个数。
引用
@article{arxiv.2105.08394,
title = {The slice rank of a direct sum},
author = {W. T. Gowers},
journal= {arXiv preprint arXiv:2105.08394},
year = {2021}
}
备注
This corrects an earlier version, with a proof that proceeds along much more standard lines. The result is therefore less interesting than it might have seemed, but worth recording at least in preprint form in case it is ever needed