Saved in:
| Main Author: | |
|---|---|
| Format: | Preprint |
| Published: |
2020
|
| Subjects: | |
| Online Access: | https://arxiv.org/abs/2011.12273 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866916604643639296 |
|---|---|
| author | Duliński, Wojciech |
| author_facet | Duliński, Wojciech |
| contents | We develop the technique of geometric realizations with algebraically independent (over the field of real algebraic numbers) coordinates of vertices and combine it with the oriented volume method inspired by work of McLennan and Tourky on the Sperner's lemma. This enables us to prove new results: the non-draw property of the generalized Y game, the theorem about triangulation of the product of two simplices, multilabeled Ky Fan' s lemma, and give new proofs of known results: the multilabeled version of Sperner's lemma and generalized Atanassov conjecture. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2011_12273 |
| institution | arXiv |
| publishDate | 2020 |
| record_format | arxiv |
| spellingShingle | Homotopies and transcendental extensions in colouring problems Duliński, Wojciech Combinatorics We develop the technique of geometric realizations with algebraically independent (over the field of real algebraic numbers) coordinates of vertices and combine it with the oriented volume method inspired by work of McLennan and Tourky on the Sperner's lemma. This enables us to prove new results: the non-draw property of the generalized Y game, the theorem about triangulation of the product of two simplices, multilabeled Ky Fan' s lemma, and give new proofs of known results: the multilabeled version of Sperner's lemma and generalized Atanassov conjecture. |
| title | Homotopies and transcendental extensions in colouring problems |
| topic | Combinatorics |
| url | https://arxiv.org/abs/2011.12273 |