# Stabilizer group of generalized determinant

## TL;DR

This paper investigates the stabilizer group of a generalized determinant, a linear combination of the determinant and permanent, providing insights into its algebraic symmetry properties.

## Contribution

It introduces the concept of a generalized determinant and determines its stabilizer group, a novel contribution to algebraic symmetry analysis.

## Key findings

- Identifies the stabilizer group of the generalized determinant.
- Provides a characterization of the symmetry group.
- Extends understanding of determinant and permanent combinations.

## Abstract

In this paper, we consider linear combination of determinant and permanent, which we call generalized determinant, and determine the stabilizer group of it.