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arxiv: 1111.6404 · v3 · pith:GW5QLUYEnew · submitted 2011-11-28 · 🧮 math.CO

On the purity of maximal weakly separated set families

classification 🧮 math.CO
keywords maximalproofseparatedweaklycardinalitycombinatoricsdirectelementary
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We present a short proof that every maximal family of weakly separated subsets of $[n]$ of cardinality between $[a,b]$ have the same size. Our proof is direct and only uses elementary combinatorics of lattice paths.

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