Erdös's Matching Conjecture and $s$-wise $t$-intersection Conjecture via Symmetrical Smoothing Method
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arXiv
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| Natura: | Preprint |
| Pubblicazione: |
2014
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| _version_ | 1866915342037549056 |
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| author | Blinovsky, Vladimir |
| author_facet | Blinovsky, Vladimir |
| contents | We find the formula for the maximal cardinality of the family of $n$-tuples from ${[n]\choose k}$ with does not have $\ell$--matching. This formula after some analytical issues can be reduce to the Erdös's Matching formula. Also we prove the conjecture about the cardinality of maximal $s$-wise $t$-intersecting family of $k$-element subsets of $[n]$. In the proofs we use original method which we have already used in the proof of Miklós-Manikam-Singhi conjecture in \cite{1}. We call this method Symmetrical smoothing method, we add small corrections |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_1402_1505 |
| institution | arXiv |
| publishDate | 2014 |
| record_format | arxiv |
| spellingShingle | Erdös's Matching Conjecture and $s$-wise $t$-intersection Conjecture via Symmetrical Smoothing Method Blinovsky, Vladimir Combinatorics We find the formula for the maximal cardinality of the family of $n$-tuples from ${[n]\choose k}$ with does not have $\ell$--matching. This formula after some analytical issues can be reduce to the Erdös's Matching formula. Also we prove the conjecture about the cardinality of maximal $s$-wise $t$-intersecting family of $k$-element subsets of $[n]$. In the proofs we use original method which we have already used in the proof of Miklós-Manikam-Singhi conjecture in \cite{1}. We call this method Symmetrical smoothing method, we add small corrections |
| title | Erdös's Matching Conjecture and $s$-wise $t$-intersection Conjecture via Symmetrical Smoothing Method |
| topic | Combinatorics |
| url | https://arxiv.org/abs/1402.1505 |