All Questions

Let $Q^n := \{0,1\}^n$ be the Hamming cube with the Hamming metric. (Recall that the Hamming is defined by the distance $d(x,y) := \# \{ i : x_i \neq y_i \}$. For integers $0 \leq k \leq n$, define a ...

If there are m binary arrays (with 0 and 1) of length n, and between any two of these m arrays, there are k and only k same numbers (with the same site index in two different arrays). For example, if ...

Let $P$ be the polytope obtained as the convex hull of $n$ points in $\mathbb R^d$. This is the $V$-representation of $P$. Note that $P$ can also be represented as an intersection of closed half-...

I am currently stuck on the following problem: given a $n \times d$ Boolean matrix $X = [x_1,\ldots,x_d]$ where each $x_j =[x_{1,j},\ldots,x_{n,j}]^\top \in \{0,1\}^n$, I want to bound the number of ...