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On the Width of Lattice-Free simplices

✍ Scribed by Jean-Michel Kantor

Book ID
111524243
Publisher
Cambridge University Press
Year
1999
Tongue
English
Weight
59 KB
Volume
118
Category
Article
ISSN
0010-437X

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πŸ“œ SIMILAR VOLUMES

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We construct d-dimensional empty lattice simplices of arbitrarily high volume from (d -1)dimensional ones, while preserving the lattice width. In particular, we give an example of infinitely many empty 4-simplices of width 2.

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The following conjecture of U Faigle and B Sands is proved: For every number R > 0 there exists a number n(R) such that if 2 is a finite distributive lattice whose width w(Z) (size of the largest antichain) is at least n(R), then IZ/a Rw(Z). In words this says that as one considers ~ increasingly la