A Generalisation of Sperner's Theorem Using Weighted Chains
Fuente:
arXiv
Guardado en:
| Autores principales: | , , |
|---|---|
| Formato: | Preprint |
| Publicado: |
2025
|
| Materias: | |
| Acceso en línea: | |
| Etiquetas: |
Agregar Etiqueta
Sin Etiquetas, Sea el primero en etiquetar este registro!
|
| _version_ | 1866912618418012160 |
|---|---|
| author | Dillies, Yaël Johnson, Matthew Kowalska, Aleksandra |
| author_facet | Dillies, Yaël Johnson, Matthew Kowalska, Aleksandra |
| contents | We find the (unique) largest subset of $\{0, 1, 2\}^n$ such that it contains no two elements, one of which is coordinatewise greater than the other, but strictly greater on at most $k$ coordinates. To do so, we decompose the cube into weighted chains.
In Appendix B we present a new proof of Sperner's theorem we found while working on this problem. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2509_26493 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | A Generalisation of Sperner's Theorem Using Weighted Chains Dillies, Yaël Johnson, Matthew Kowalska, Aleksandra Combinatorics 05D05 We find the (unique) largest subset of $\{0, 1, 2\}^n$ such that it contains no two elements, one of which is coordinatewise greater than the other, but strictly greater on at most $k$ coordinates. To do so, we decompose the cube into weighted chains. In Appendix B we present a new proof of Sperner's theorem we found while working on this problem. |
| title | A Generalisation of Sperner's Theorem Using Weighted Chains |
| topic | Combinatorics 05D05 |
| url | https://arxiv.org/abs/2509.26493 |