Author pages are created from data sourced from our academic publisher partnerships and public sources.

Publications Influence

Graphs of difference operators for p-ary sequences

- A. Garber
- Mathematics
- 28 November 2007

Abstract
For a given prime p and positive integer n, we consider the graph Gn of the difference operator acting on p-ary sequences of length n. We suggest new proofs of some results of V.I. Arnold on… Expand

6 3

Symmetries of Monocoronal Tilings

- D. Frettlöh, A. Garber
- Mathematics, Computer Science
- Discret. Math. Theor. Comput. Sci.
- 19 February 2014

TLDR

2 2- PDF

The complete classification of five-dimensional Dirichlet-Voronoi polyhedra of translational lattices.

- Mathieu Dutour Sikirić, A. Garber, A. Schürmann, C. Waldmann
- Mathematics, Medicine
- Acta crystallographica. Section A, Foundations…
- 30 June 2015

This paper reports on the full classification of Dirichlet-Voronoi polyhedra and Delaunay subdivisions of five-dimensional translational lattices. A complete list is obtained of 110 244 affine types… Expand

13 1- PDF

On the origin of crystallinity: a lower bound for the regularity radius of Delone sets.

- I. A. Baburin, Mikhail Bouniaev, +4 authors E. Schulte
- Mathematics, Medicine
- Acta crystallographica. Section A, Foundations…
- 13 April 2018

The mathematical conditions for the origin of long-range order or crystallinity in ideal crystals are one of the very fundamental problems of modern crystallography. It is widely believed that the… Expand

8- PDF

On $${\pi}$$π-Surfaces of Four-Dimensional Parallelohedra

- A. Garber
- Mathematics
- 29 September 2013

We show that every four-dimensional parallelohedron P satisfies a recently found condition of Garber, Gavrilyuk & Magazinov sufficient for the Voronoi conjecture being true for P. Namely, we show… Expand

2- PDF

The Voronoi Conjecture for Parallelohedra with Simply Connected $$\delta $$δ-Surfaces

- A. Garber, A. Gavrilyuk, A. Magazinov
- Mathematics, Computer Science
- Discret. Comput. Geom.
- 5 December 2012

TLDR

9- PDF

Pisot substitution sequences, one dimensional cut-and-project sets and bounded remainder sets with fractal boundary

- D. Frettloh, A. Garber
- Mathematics
- 4 November 2017

This paper uses a connection between bounded remainder sets in $\mathbb{R}^d$ and cut-and-project sets in $\mathbb{R}$ together with the fact that each one-dimensional Pisot substitution sequence is… Expand

5- PDF

Another Ham Sandwich in the Plane

- Alexey Balitskiy, A. Garber, R. Karasev
- Mathematics
- 29 July 2013

We show that every two nice measures in the plane can be partitioned into equal halves by translation of an angle from any k-fan when k is odd and in some cases when k is even. We also give some… Expand

1- PDF

On Helly number for crystals and cut-and-project sets

- A. Garber
- Mathematics
- 25 May 2016

We prove existence of finite Helly numbers for crystals and for cut-and-project sets with convex windows; also we prove exact bound of $k+6$ for the Helly number of a crystal consisting of $k$ copies… Expand

2- PDF

Structural model for Fe-containing human acireductone dioxygenase

- T. Pochapsky, X. Liu, A. R. Deshpande, D. Ringe, A. Garber, J. Ryan
- Chemistry
- 18 November 2020