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The Rank Polynomials of Large Random Lattices

✍ Scribed by Grimmett, G. R.

Book ID
120096672
Publisher
Oxford University Press
Year
1978
Tongue
English
Weight
195 KB
Volume
s2-18
Category
Article
ISSN
0024-6107

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πŸ“œ SIMILAR VOLUMES

The level polynomials of the free distri
The level polynomials of the free distributive lattices
✍ George Markowsky πŸ“‚ Article πŸ“… 1980 πŸ› Elsevier Science 🌐 English βš– 915 KB

We show that there exist a set of polynomials {Lk 1 k = 0, 1 \* \* a} such that L,(n) is the number of elements of rank k in the free distributive lattice on n generators. L,(n) = L,(n) = 1 for all n and the degree of L, is k -1 for k 5 1. We show that the coefficients of the L, can be calculated us

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Extensible integration lattices have the attractive property that the number of points in the node set may be increased while retaining the existing points. It is shown here that there exist generating vectors, h; for extensible rank-1 lattices such that for n ΒΌ b; b 2 ; y points and dimensions s ΒΌ

The Ajtai random class of lattices
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Ajtai has recently given a reduction from the problem of approximating a short basis for a lattice in the worst case, to the problem of ΓΏnding a short lattice vector for a uniformly chosen lattice in a certain random class of lattices. Here we give an explicit formula for the number of lattices of t