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A poset or partially ordered set is a set endowed with a partial order, meaning a binary relation $\leq$ which is reflexive ($x \leq x$ for all $x$), antisymmetric ($x\leq y$ and $y\leq x$ implies $x=y$), and transitive ($x\leq y$ and $y\leq z$ implies $x \leq z$).
2
votes
1
answer
83
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Birkhoff Lattice of a forest
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 …
3
votes
1
answer
199
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Matching in the Boolean Algebra
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 …
2
votes
Matching in the Boolean Algebra
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 …