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 Jan13 answered Number of upward closed subsets Oct3 comment Distribute n balls across m bags when bags are not empty to get the same sizes Finally, each box contains either $\lfloor \frac{N}{m} \rfloor$ or $\lfloor \frac{N}{m} \rfloor +1$ balls. As the first step, we fill $i$ th box with $\lfloor \frac{N}{m} \rfloor -n_i$ balls for all $i$, so that each box contains $\lfloor \frac{N}{m} \rfloor$ balls. We are left with $r:=N-\lfloor \frac{N}{m} \rfloor$ balls, that can be distributed in $\binom{m}{r}$ ways. I hope this clarifies. Sep30 answered Distribute n balls across m bags when bags are not empty to get the same sizes Sep24 awarded Autobiographer Aug22 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. Aug22 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. Aug22 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 $\{2\} \subset \{2,3\} \subset \{2,3,1\} \subset \{2,3,1,4\}$ Aug1 comment Average deviation of group sizes Is $\delta$ some arbitrary number here? Jul26 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.) Jul26 asked minimum number of unit distances required for a unit equilateral triangle Jul25 comment How to calculate the number of integer solution of a linear equation with constraints? See lemma 2 here Jul23 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. Jul23 answered Combination with restriction Jul21 comment maximum size of a $k$-intersecting family of $[n]$ Thanks for your answer. I could not have asked for more. Jul19 awarded Benefactor Jul19 accepted maximum size of a $k$-intersecting family of $[n]$ Jul18 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. Jul16 comment How many squares can be formed from n equidistant points in a circle? did you mean, uniformly spaced on the circumference? Jul16 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. Jul16 revised Tough combinatorics problem added 75 characters in body