Simple proofs of estimations of Ramsey numbers and of discrepancy
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arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2021
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| _version_ | 1866908744925839360 |
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| author | Buchaev, A. Skopenkov, A. |
| author_facet | Buchaev, A. Skopenkov, A. |
| contents | In this expository note we present simple proofs of the lower bound of Ramsey numbers (Erdös theorem), and of the estimation of discrepancy. Neither statements nor proofs require any knowledge beyond high-school curriculum (except a minor detail). Thus they are accessible to non-specialists, in particular, to students. Our exposition is simpler than the standard exposition because no probabilistic language is used. In order to prove the existence of a `good' object we prove that the number of `bad' objects is smaller than the number of all objects. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2107_13831 |
| institution | arXiv |
| publishDate | 2021 |
| record_format | arxiv |
| spellingShingle | Simple proofs of estimations of Ramsey numbers and of discrepancy Buchaev, A. Skopenkov, A. Combinatorics Discrete Mathematics History and Overview 05-01, 05D10, 05D40 In this expository note we present simple proofs of the lower bound of Ramsey numbers (Erdös theorem), and of the estimation of discrepancy. Neither statements nor proofs require any knowledge beyond high-school curriculum (except a minor detail). Thus they are accessible to non-specialists, in particular, to students. Our exposition is simpler than the standard exposition because no probabilistic language is used. In order to prove the existence of a `good' object we prove that the number of `bad' objects is smaller than the number of all objects. |
| title | Simple proofs of estimations of Ramsey numbers and of discrepancy |
| topic | Combinatorics Discrete Mathematics History and Overview 05-01, 05D10, 05D40 |
| url | https://arxiv.org/abs/2107.13831 |