A sumset version of a conjecture of Pilz
Fuente:
arXiv
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| Autores principales: | , |
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| Formato: | Preprint |
| Publicado: |
2024
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| Acceso en línea: | |
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| _version_ | 1866914955244077056 |
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| author | Nagy, János Pach, Péter Pál |
| author_facet | Nagy, János Pach, Péter Pál |
| contents | Pilz's conjecture states that for any finite set $A=\{a_1,a_2,\dots,a_k\}$ of positive integers and positive integer $n$ in the union of the sets $\{a_1,2a_1,\dots,na_1\},\dots, \{a_k,2a_k,\dots,na_k\}$ (considered as a multiset) at least $n$ values appear an odd number of times. In this short note we consider a variant of this problem. Namely, we show that in the sumset $\{a_1,2a_1,\dots,na_1\}+\dots+\{a_k,2a_k,\dots,na_k\}$ (considered as a multiset) at least $n$ values appear an odd number of times. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2409_15075 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | A sumset version of a conjecture of Pilz Nagy, János Pach, Péter Pál Combinatorics Number Theory Pilz's conjecture states that for any finite set $A=\{a_1,a_2,\dots,a_k\}$ of positive integers and positive integer $n$ in the union of the sets $\{a_1,2a_1,\dots,na_1\},\dots, \{a_k,2a_k,\dots,na_k\}$ (considered as a multiset) at least $n$ values appear an odd number of times. In this short note we consider a variant of this problem. Namely, we show that in the sumset $\{a_1,2a_1,\dots,na_1\}+\dots+\{a_k,2a_k,\dots,na_k\}$ (considered as a multiset) at least $n$ values appear an odd number of times. |
| title | A sumset version of a conjecture of Pilz |
| topic | Combinatorics Number Theory |
| url | https://arxiv.org/abs/2409.15075 |