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On Disjoint Chains of Subsets

✍ Scribed by Eric Lehman; Dana Ron

Publisher
Elsevier Science
Year
2001
Tongue
English
Weight
166 KB
Volume
94
Category
Article
ISSN
0097-3165

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✦ Synopsis

We prove the following theorem concerning the poset of all subsets of [n] ordered by inclusion. Consider any two equal-size families of subsets of [n], S and R, where within each family all subsets have the same number of elements. Suppose there exists a bijection ,: S [ R such that A#f (A) for all A # S. Then there exist |S| disjoint saturated chains containing all the subsets in S and R.

2001

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