It is a long story I just make it short. First I will star with permutation. Let $S$ denote the group of all possible permutations of $C$. Let $A$ be the subset of all acceptable permutation for $C$, where $A \subset S$. $A$ is said to be t-intersecting if all permutation in $A$, lets call it $s_n$, $s_n$ $\in$ $A$ agree on at least t points, where $ \mid t \mid \leq H$. $H$ can be any number. It is natural to ask, how small, and large can an intersecting in $A$? An example of a small intersecting of permutations is when the number of intersection is the lower bound $ \mid t \mid < H$ of the hidden comments. An example of a large intersecting is when $ \mid t \mid = H$.
let's say H is the value of the intersection. For example, if H=3, then the lower bond of the intersection is 1, and the upper bound is 3. Now, t is the intersection of all permutation in A and bounded by the lower and upper bound of H. In this example, if t=1, it means, there is one common element in all permutation of A, $ \mid t \mid < H$ . Assume, there is a linear function that gives the same result of t. I mean, if the intersection shows there is one common element in all permutation of A, then linear function also shows the same number of common element. How we can prove that the linear function gives the intersection result?