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This is a Quantitative Study study.

October 2, 2025Open Access

On the Range of the Permanent of (±1)-Matrices

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This research establishes a superpolynomial lower bound on the range of the permanent function.
The lower bound indicates significant complexity in computing the permanent for these matrices.
The analysis focuses on $n \times n$ matrices with entries that are either +1 or -1.
The findings imply challenges in algorithmic approaches to determine the permanent function.

Implication

This analysis establishes a superpolynomial lower bound on the permanent function's range in $n \times n$ matrices, suggesting complexities in its computation.

Abstract

We establish a superpolynomial lower bound on the range of the permanent function on the set of n× n matrices with ±1 entries.

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Cite This Study

Ingram et al. (2025) studied this question.

synapsesocial.com/papers/68de5da283cbc991d0a20778 https://doi.org/10.48550/arxiv.2507.09433

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Implication

This analysis establishes a superpolynomial lower bound on the permanent function's range in $n \times n$ matrices, suggesting complexities in its computation.

Abstract

We establish a superpolynomial lower bound on the range of the permanent function on the set of n× n matrices with ±1 entries.

On the Range of the Permanent of (±1)-Matrices

Key Points

Implication

Abstract

Discussion

Cite This Study

On the Range of the Permanent of (±1)-Matrices

Key Points

Implication

Abstract

Discussion

Cite This Study

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