שמור ב:
| Main Authors: | , |
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| פורמט: | Preprint |
| יצא לאור: |
2023
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| נושאים: | |
| גישה מקוונת: | https://arxiv.org/abs/2312.04439 |
| תגים: |
הוספת תג
אין תגיות, היה/י הראשונ/ה לתייג את הרשומה!
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תוכן הענינים:
- Endowed with the binary operation of set addition, the family $\mathcal P_{{\rm fin},0}(\mathbb N)$ of all finite subsets of $\mathbb N$ containing $0$ forms a monoid, with the singleton $\{0\}$ as its neutral element. We show that the only non-trivial automorphism of $\mathcal P_{{\rm fin},0}(\mathbb N)$ is the involution $X \mapsto \max X - X$. The proof leverages ideas from additive number theory and proceeds through an unconventional induction on what we call the boxing dimension of a finite set of integers, that is, the smallest number of (discrete) intervals whose union is the set itself.