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A Homological Lower Bound for Order Dimension of Lattices

✍ Scribed by Victor Reiner; Volkmar Welker

Book ID
110234260
Publisher
Springer Netherlands
Year
1999
Tongue
English
Weight
47 KB
Volume
16
Category
Article
ISSN
0167-8094

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A system F of functions [1, 2, ..., n] Γ„ [1, 2, ..., k] has Natarajan dimension at most d if no (d+1)-element subset A/X is 2-shattered. A is 2-shattered if for each x # A there is a 2-element set V x [1, 2, ..., k] such that for any choice of elements c x # V x , a function f # F exists with f (x)=