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Improved bounds on the Product Rank of the Permanent
Authors
Edinah Gnang
Rongyu Xu
Publication date
10 November 2023
Publisher
View
on
arXiv
Abstract
We unify Ryser's and Glynn's formulas for computing the permanent into a single framework. We then show via an orbital bound argument that the product rank of the permanent is asymptotically upper bounded by
exp
β‘
(
Ο
2
n
3
)
4
3
n
\frac{\exp\left(\pi\sqrt{\frac{2n}{3}}\right)}{4\sqrt{3}n}
4
3
β
n
e
x
p
(
Ο
3
2
n
β
β
)
β
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oai:arXiv.org:2311.05890
Last time updated on 10/02/2024