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I am given a set $M\subseteq\{1,\dots,n\},\,|M|=m$ and a famliy of $k$-sets ($k<m$) $\mathcal{U}=\{U_1,\dots,U_p\},\,U_{i}\subset M$. For this family, I would like to check one of the following condit …

Suppose you have the $K_{2n}$ covered by a multigraph consisting of $2n-1$ bicliques, each consisting of a partition of the vertex set into two sets of equal size. Here is a picture of $K_{6}$ with 5 …

In my research, I stumbled upon a particular kind of poset and I was wondering, whether there is something in the literature (I could not find anything so far). They are distributive lattice $L$ suc …

We consider the Boolean Algebra of the set $[n]=\{1,\dots,n\}$ and the matching $\psi$ from the $m+1$ subsets of $[n]$ into the $m$ subsets of $[n]$ for $(n+1)/2\leq m+1\leq n$, which is used to show …

One can understand the image of $\psi$ or $\psi|_M$ in terms of the inverse map $\phi$. $\phi$ maps an $m$ set to an $(m+1)$ set (if possible) in the following way. If $$A=\{i_1,\dots,i_m\}$$ is our …