Size of collection of $k$-element subsets of $n$-element set whose pairwise intersections are at most 2.

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I am trying to determine the maximum possible size of a collection of $k$-element subsets of $1, 2, cdots n$ set whose pairwise intersections are at most 2.



It's clear that when $k = 3$, its just the number of distinct three element subsets of $1, 2, cdots n$ = $binomn3$. I've also been counting them out for smaller cases and don't see the pattern.



Edit: I've searched through all the suggested questions that arose when I was asking my question and found nothing that helps me find bounds or a precise solution.




extremal-combinatorics




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    The Ray-Chaudhuri-Wilson Theorem gives you the upper bound $binomn3$ for all $k$-subsets of $1,2,dots,n$. Maybe, this answers helps you: math.stackexchange.com/a/2323/296687
    – user160919
    Jul 20 at 8:37














up vote
3
down vote

favorite
1












I am trying to determine the maximum possible size of a collection of $k$-element subsets of $1, 2, cdots n$ set whose pairwise intersections are at most 2.



It's clear that when $k = 3$, its just the number of distinct three element subsets of $1, 2, cdots n$ = $binomn3$. I've also been counting them out for smaller cases and don't see the pattern.



Edit: I've searched through all the suggested questions that arose when I was asking my question and found nothing that helps me find bounds or a precise solution.




extremal-combinatorics




share|cite|improve this question















  • 1




    The Ray-Chaudhuri-Wilson Theorem gives you the upper bound $binomn3$ for all $k$-subsets of $1,2,dots,n$. Maybe, this answers helps you: math.stackexchange.com/a/2323/296687
    – user160919
    Jul 20 at 8:37












up vote
3
down vote

favorite
1









up vote
3
down vote

favorite
1






1





I am trying to determine the maximum possible size of a collection of $k$-element subsets of $1, 2, cdots n$ set whose pairwise intersections are at most 2.



It's clear that when $k = 3$, its just the number of distinct three element subsets of $1, 2, cdots n$ = $binomn3$. I've also been counting them out for smaller cases and don't see the pattern.



Edit: I've searched through all the suggested questions that arose when I was asking my question and found nothing that helps me find bounds or a precise solution.




extremal-combinatorics




share|cite|improve this question











I am trying to determine the maximum possible size of a collection of $k$-element subsets of $1, 2, cdots n$ set whose pairwise intersections are at most 2.



It's clear that when $k = 3$, its just the number of distinct three element subsets of $1, 2, cdots n$ = $binomn3$. I've also been counting them out for smaller cases and don't see the pattern.



Edit: I've searched through all the suggested questions that arose when I was asking my question and found nothing that helps me find bounds or a precise solution.





extremal-combinatorics





share|cite|improve this question










share|cite|improve this question




share|cite|improve this question









asked Jul 17 at 16:13









Yunus Syed

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  • 1




    The Ray-Chaudhuri-Wilson Theorem gives you the upper bound $binomn3$ for all $k$-subsets of $1,2,dots,n$. Maybe, this answers helps you: math.stackexchange.com/a/2323/296687
    – user160919
    Jul 20 at 8:37












  • 1




    The Ray-Chaudhuri-Wilson Theorem gives you the upper bound $binomn3$ for all $k$-subsets of $1,2,dots,n$. Maybe, this answers helps you: math.stackexchange.com/a/2323/296687
    – user160919
    Jul 20 at 8:37







1




1




The Ray-Chaudhuri-Wilson Theorem gives you the upper bound $binomn3$ for all $k$-subsets of $1,2,dots,n$. Maybe, this answers helps you: math.stackexchange.com/a/2323/296687
– user160919
Jul 20 at 8:37




The Ray-Chaudhuri-Wilson Theorem gives you the upper bound $binomn3$ for all $k$-subsets of $1,2,dots,n$. Maybe, this answers helps you: math.stackexchange.com/a/2323/296687
– user160919
Jul 20 at 8:37















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