Shrinkability of Minimal Elements in Sphere Representations of Posets
Tóm tắt
Let k be a positive integer and let P = (X,≤) be a poset. We call P a k-sphere order provided there is a mapping f which assigns to each element x
$$ \in$$
X a ball f(x) in Rk so that x ≤ y in P if and only if f(x)
$$ \subseteq$$
f(y). We ask: Given that P is a k-sphere order, does there necessarily exist a representation f with the property that every minimal element of P is assigned a ball of radius zero? The answer is “yes” for k = 1, but “no” for all k ≥ 2.
Tài liệu tham khảo
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