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Based on the answer and comments by @Corentin B, I believe the following upper bound holds: $$ C_{k,t}^n \leq D_t \binom{n-1}{t}\cdot t! \cdot S(k/2,t) $$ for $k \in 2 \mathbb N$ and $t \le k/2$, wher …

We are interested in a class of walks on the complete graph on $[n] = \{1,2,\dots,n\}$. A walk of length $k$ is an ordered tuple of directed edges $$ ((i_1,i_2),(i_2,i_3),\ldots,(i_k,i_{k+1})) $$ wher …

Assume that we have a set system $\mathfrak T = \{\mathcal T_1, \mathcal T_2, \dots, \mathcal T_N \}$ where each $\mathcal T_k$ is a collection of subsets of $[n] := \{1,\dots,n\}$ of the form $$ \ma …

Consider the set of all $k$-subsets of $\{1,\dots,n\}$, naturally identified with a subset $A$ of $\{0,1\}^n$ where each element has exactly $k$ ones. Is there a sharp bound known for $\epsilon$-cover …

Suppose we have a graph on $n$ nodes. We would like to assign to each node either a $+1$ or a $-1$. Call this a configuration $\sigma \in \{+1,-1\}^n$. The number of $+1$s that we have to assign is ex …