# Questions tagged [extremal-set-theory]

The tag has no usage guidance.

31 questions
233 views

### Domination problem with sets

For nearly two years, I have been struggling with the next task I have already published on MSE, but unfortunately with no respond. Let $M$ be a non-empty and finite set, $S_1,...,S_k$ subsets ...
36 views

### Is the finite projective plane stable as an extremal set system?

Let $\Sigma$ be a set of $|\Sigma| = n$ subsets of the universe $[n]$, each of size $k$, with the property that any two of these subsets intersect on at most one element. It is easy to see that the ...
77 views

### Number of distinct 3-sets formed as subsets of a 4-uniform set family

Let $\mathcal{F} \subseteq \binom{[n]}{4}$ be a collection of size-4 subsets of $\{1,\ldots,n\}$, i.e., a 4-uniform set family. Let $\mathcal{F'}$ be the collection of size-3 sets for which a ...
99 views

### Abundance in union closed families

For any finite set $S$ and every partition $S_1, \dots, S_n$ of $S$, let $P(S_1, \dots, S_n)$ be the family consisting of all possible unions of $S_1, \dots, S_n$. Clearly, $P(S_1, \dots, S_n)$ is a ...
203 views

### the size of a down-set?

I'm reading a research article lately, and got confused about a question. So, the fundamental theorem of Kruskal and Katona states that if each set in a given set system $\mathcal{A}$ has $k$ ...
257 views

### Set family $\mathcal{F}$ such that for all $A,B,C \in \mathcal{F}$ both $A \cap B \not \subseteq C$ and $C \not \subseteq A \cup B$

This question initially arose out of a question in asymptotic matroid theory. The matroid question has since been answered in a different way, but the extremal set theory question remains unanswered ...
95 views

### A Combinatorial Problem on Extremal Set Theory

Given a ground set $[n]$, under what condition of parameters $a,b,c$ does a family of subsets $\mathcal{F}\subseteq 2^{[n]}$ with the following property exist? (i) $\forall S\in \mathcal{F}$, $|S|=a$....
79 views

### Upper bound for the size of a $k$-uniform $s$-wise $t$-intersecting set system
Given integers $n \geq k \geq t \geq 1$ and an integer $s$, let $m(n,k,s,t)$ denote the maximum size of a family $\mathcal F$ of $k$-subsets of $[n]$, i.e. $\mathcal F \subseteq \binom{[n]}{k}$, such ...