Distinguish permutations

István Szalkai

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arXiv · 2512.20673

Distinguish permutations

István Szalkai

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Abstract

We are looking for integer numbers $g_{j}$ and $x_{j}$ ($j=1,...,n$) such that the sums $T_{\pi} := \sum_{j=1}^{n} g_{j} \cdot x_{\pi\left( j\right) }$ are different for all permutations $\pi\in S_{n}$ and $\max\left\{T_{\pi}:\pi\in S_{n}\right\} $ is as small as possible.

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István Szalkai. 2025-12-19. Distinguish permutations. https://arxiv.org/abs/2512.20673

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