0
$\begingroup$

Consider a set $S=\{1, \dots, n\}$. I want to estimate the length $l$ of the longest sequence of disjoint subsets of size $k$.

In other words I need the length of the sequence: $seq= ((a_{1_1}, \dots, a_{1_k}), (a_{2_1}, \dots, a_{2_k} ), ... (a_{l_1}, \dots, a_{l_k})) $ where $a_{i_j} \neq a_{u_v} \forall u, v, i, j$

observe that if we remove the condition that the subset must be disjoint then it reduces to the binomial coefficient $l= \binom{n}{k}$

Question 1:

Does $l$ depends on the choice of the $k$ subsets?

Question 2:

Is it possible to compute the maximal and minimal possible length of the sequence?

  • 1
    I don't understand the question, isn't the length just $\lfloor n/k \rfloor$? – 2017-02-09
  • 0
    O I think you may be right. I am probably sleeping – 2017-02-09

0 Answers 0