Matches in SemOpenAlex for { <https://semopenalex.org/work/W2987347858> ?p ?o ?g. }
Showing items 1 to 79 of
79
with 100 items per page.
- W2987347858 abstract "For an integer $d geq 2$, a family $mathcal{F}$ of sets is $textit{$d$-wise intersecting}$ if for any distinct sets $A_1,A_2,dots,A_d in mathcal{F}$, $A_1 cap A_2 cap dots cap A_d neq emptyset$, and $textit{non-trivial}$ if $bigcap mathcal{F} = emptyset$. Hilton and Milner conjectured that for $k geq d geq 2$ and large enough $n$, the extremal non-trivial $d$-wise intersecting family of $k$-element subsets of $[n]$ is one of the following two families: begin{align*} &mathcal{H}(k,d) = {A in binom{[n]}{k} : [d-1] subset A, A cap [d,k+1] neq emptyset} cup {[k+1] setminus {i } : i in [d - 1]} &mathcal{A}(k,d) = { A in binom{[n]}{k} : |A cap [d+1]| geq d }. end{align*} The celebrated Hilton-Milner Theorem states that $mathcal{H}(k,2)$ is the unique extremal non-trivial intersecting family for $k>3$. We prove the conjecture and prove a stability theorem, stating that any large enough non-trivial $d$-wise intersecting family of $k$-element subsets of $[n]$ is a subfamily of $mathcal{A}(k,d)$ or $mathcal{H}(k,d)$." @default.
- W2987347858 created "2019-11-22" @default.
- W2987347858 creator A5015606585 @default.
- W2987347858 creator A5024446850 @default.
- W2987347858 date "2019-11-04" @default.
- W2987347858 modified "2023-09-27" @default.
- W2987347858 title "Non-trivial $d$-wise Intersecting families" @default.
- W2987347858 cites W1964094911 @default.
- W2987347858 cites W1992844673 @default.
- W2987347858 cites W2050953287 @default.
- W2987347858 cites W2091239462 @default.
- W2987347858 cites W2100896331 @default.
- W2987347858 cites W2119135810 @default.
- W2987347858 cites W2154774722 @default.
- W2987347858 cites W2606666068 @default.
- W2987347858 cites W2762912304 @default.
- W2987347858 cites W3105688314 @default.
- W2987347858 cites W3143189643 @default.
- W2987347858 cites W393299573 @default.
- W2987347858 hasPublicationYear "2019" @default.
- W2987347858 type Work @default.
- W2987347858 sameAs 2987347858 @default.
- W2987347858 citedByCount "0" @default.
- W2987347858 crossrefType "posted-content" @default.
- W2987347858 hasAuthorship W2987347858A5015606585 @default.
- W2987347858 hasAuthorship W2987347858A5024446850 @default.
- W2987347858 hasConcept C104317684 @default.
- W2987347858 hasConcept C114614502 @default.
- W2987347858 hasConcept C121332964 @default.
- W2987347858 hasConcept C17744445 @default.
- W2987347858 hasConcept C185592680 @default.
- W2987347858 hasConcept C199360897 @default.
- W2987347858 hasConcept C199539241 @default.
- W2987347858 hasConcept C200288055 @default.
- W2987347858 hasConcept C2780990831 @default.
- W2987347858 hasConcept C33923547 @default.
- W2987347858 hasConcept C41008148 @default.
- W2987347858 hasConcept C50929876 @default.
- W2987347858 hasConcept C55493867 @default.
- W2987347858 hasConcept C97137487 @default.
- W2987347858 hasConceptScore W2987347858C104317684 @default.
- W2987347858 hasConceptScore W2987347858C114614502 @default.
- W2987347858 hasConceptScore W2987347858C121332964 @default.
- W2987347858 hasConceptScore W2987347858C17744445 @default.
- W2987347858 hasConceptScore W2987347858C185592680 @default.
- W2987347858 hasConceptScore W2987347858C199360897 @default.
- W2987347858 hasConceptScore W2987347858C199539241 @default.
- W2987347858 hasConceptScore W2987347858C200288055 @default.
- W2987347858 hasConceptScore W2987347858C2780990831 @default.
- W2987347858 hasConceptScore W2987347858C33923547 @default.
- W2987347858 hasConceptScore W2987347858C41008148 @default.
- W2987347858 hasConceptScore W2987347858C50929876 @default.
- W2987347858 hasConceptScore W2987347858C55493867 @default.
- W2987347858 hasConceptScore W2987347858C97137487 @default.
- W2987347858 hasOpenAccess W2987347858 @default.
- W2987347858 hasRelatedWork W2054397115 @default.
- W2987347858 hasRelatedWork W2290284830 @default.
- W2987347858 hasRelatedWork W2334696714 @default.
- W2987347858 hasRelatedWork W2492077975 @default.
- W2987347858 hasRelatedWork W2502916942 @default.
- W2987347858 hasRelatedWork W2783983302 @default.
- W2987347858 hasRelatedWork W2886326260 @default.
- W2987347858 hasRelatedWork W2949145468 @default.
- W2987347858 hasRelatedWork W2952826922 @default.
- W2987347858 hasRelatedWork W2954678432 @default.
- W2987347858 hasRelatedWork W2963265845 @default.
- W2987347858 hasRelatedWork W2964068385 @default.
- W2987347858 hasRelatedWork W2964295908 @default.
- W2987347858 hasRelatedWork W3031586851 @default.
- W2987347858 hasRelatedWork W3110642616 @default.
- W2987347858 hasRelatedWork W3134803083 @default.
- W2987347858 hasRelatedWork W3139088638 @default.
- W2987347858 hasRelatedWork W3158244516 @default.
- W2987347858 hasRelatedWork W3213625253 @default.
- W2987347858 hasRelatedWork W2556820943 @default.
- W2987347858 isParatext "false" @default.
- W2987347858 isRetracted "false" @default.
- W2987347858 magId "2987347858" @default.
- W2987347858 workType "article" @default.