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gmail address: sri.teach


Aug
22
comment Sperner family intersection with chains.
A better question to ask here would be: Can we classify the maximal antichains such that they intersect with every maximal chain? I expect the answer to be: An antichain intersects with every maximal chain only if it contains all subsets of a particular size.
Aug
22
comment Sperner family intersection with chains.
All subsets of same size form a maximal antichain. This has exactly one element common with any maximal chain.
Aug
22
comment Sperner family intersection with chains.
I reckon that the fact is incorrect: Consider the poset of subsets of $\{1,2,3,4\}$. The maximal antichain $\{\{1\},\{2,3,4\}\}$ has no element common with the maximal chain $\{2\} \subset \{2,3\} \subset \{2,3,1\} \subset \{2,3,1,4\}$
Aug
1
comment Average deviation of group sizes
Is $\delta$ some arbitrary number here?
Jul
26
comment minimum number of unit distances required for a unit equilateral triangle
If $n$ points are placed on the $x$-axis at integer points, there will be $n-1$ unit distances and we do not have an equilateral triangle. But, we do not have "all" unit distances. (By the time I typed this comment, I could no longer see vadim's comment to which I intended to reply.)
Jul
26
asked minimum number of unit distances required for a unit equilateral triangle
Jul
25
comment How to calculate the number of integer solution of a linear equation with constraints?
See lemma 2 here
Jul
23
comment Combination with restriction
I found that the bound is achieved if the steiner system $(n,m,l)$ exists. I have deleted my comment and posted it as an answer.
Jul
23
answered Combination with restriction
Jul
21
comment maximum size of a $k$-intersecting family of $[n]$
Thanks for your answer. I could not have asked for more.
Jul
19
awarded  Benefactor
Jul
19
accepted maximum size of a $k$-intersecting family of $[n]$
Jul
18
comment maximum size of a $k$-intersecting family of $[n]$
+1 Thanks for your answer. Most of the problems discusses in the paper seem to concern the family of subsets from $\binom{[n]}{k}$ and not the set of all subsets.
Jul
16
comment How many squares can be formed from n equidistant points in a circle?
did you mean, uniformly spaced on the circumference?
Jul
16
comment How many squares can be formed from n equidistant points in a circle?
I reckon, for $n=6$, we do not get any squares. Please do clarify by writing a picture. Square is formable iff $4|n$ and $n\ge 4$. Further, there are $\frac{n-4}{4}+1$ distinct squares.
Jul
16
revised Tough combinatorics problem
added 75 characters in body
Jul
16
answered Tough combinatorics problem
Jul
15
comment The rows continue to be different to each other
Thanks for the nice answer. Would it be better to start with s1 instead of $s_0$ (since $s_0$ has no meaning as such)? If all elements in the first column are equal, then we can delete that column. So we assume that there are at least two distinct elements in the first column and hence $s_1=2$
Jul
15
awarded  Promoter
Jul
15
comment Tough combinatorics problem
Would you specify what 'match exactly $k$ of them with letters from our string' mean? Suppose we have $a+b+c=j$ where $a$ things of type $A$, $b$ things of type $B$ and $c$ things of type $C$. Then, is $k=a\cdot s_a+b\cdot s_b+c\cdot s_c$ ?