Permanents of $3\times3$ Invertible Matrices Modulo $n$

Ayush Bohra; A. Satyanarayana Reddy

arXiv:2105.03602·math.GM·May 11, 2021

Permanents of $3\times3$ Invertible Matrices Modulo $n$

Ayush Bohra, A. Satyanarayana Reddy

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TL;DR

This paper investigates the distribution of determinants (permanents) of invertible 3x3 matrices over modular integers, providing counts of matrices with a given permanent modulo n.

Contribution

It introduces a method to count invertible 3x3 matrices over rac{Z}{nZ} with a specified permanent value, extending understanding of matrix properties modulo n.

Findings

01

Derived formulas for counting matrices with a given permanent modulo n

02

Established the distribution of permanents among invertible matrices

03

Provided explicit counts for various n and permanent values

Abstract

We count the number of elements in the set $G_{3} (n, x) = {M \in G L_{3} (Z_{n}) ∣ p er m (M) \equiv x (mod n)} .$

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Taxonomy

TopicsFinite Group Theory Research · Coding theory and cryptography · Advanced Algebra and Geometry