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.
On Simplicity of the Maximal Eigenvalue
β Scribed by Bojan Kuzma
- Publisher
- Elsevier Science
- Year
- 2001
- Tongue
- English
- Weight
- 81 KB
- Volume
- 259
- Category
- Article
- ISSN
- 0022-247X
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β¦ Synopsis
It is shown that a maximal eigenvalue of a rank-one perturbed, compact, self-adjoint operator is automatically simple, if the norm of perturbation is large enough.
π SIMILAR VOLUMES
The classic Sperner lemma states that in a simplicial subdivision of a simplex in R n and a labelling rule satisfying some boundary condition there is a completely labeled simplex. In this paper we first generalize the concept of completely labeled simplex to the concept of a balanced simplex. Using
## Finite groups, maximal class MSC (2010) 20D15 Let R be the ring Z[x]/ x p -1 x -1 = Z[x] and let a be the ideal of R generated by (x -1). In this paper, we discuss the structure of the Z[Cp ]-module (R/a n -1 )β§(R/a n -1 ), which plays an important role in the theory of p-groups of maximal cla