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SUMMARY:Jonas Jankauskas (Vilnius University)
DTSTART:20220201T133000Z
DTEND:20220201T143000Z
DTSTAMP:20260423T021226Z
UID:OWNS/76
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/OWNS/76/">Di
 git systems with rational base matrix over lattices</a>\nby Jonas Jankausk
 as (Vilnius University) as part of One World Numeration seminar\n\n\nAbstr
 act\nLet $A$ be a matrix with rational entries and no eigenvalue in absolu
 te value smaller than 1. Let $\\mathbb{Z}^d[A]$ be the minimal $A$-invaria
 nt $\\mathbb{Z}$-module\, generated by integer vectors and the matrix $A$.
  In 2018\, we have shown that one can find a finite set $D$ of vectors\, s
 uch that each element of $\\mathbb{Z}^d[A]$ has a finite radix expansion i
 n base $A$ using only the digits from $D$\, i.e. $\\mathbb{Z}^d[A]=D[A]$. 
 This is called 'the finiteness property' of a digit system. In the present
  talk I will review more recent developments in mathematical machinery\, t
 hat enable us to build finite digit systems over lattices using reasonably
  small digit sets\, and even to do some practical computations with them o
 n a computer. Tools that we use are the generalized rotation bases with di
 git sets that have 'good' convex properties\, the semi-direct ('twisted') 
 sums of such rotational digit systems\, and the special\, 'restricted' ver
 sion of the remainder division that preserves the lattice $\\mathbb{Z}^d$ 
 and can be extended to $\\mathbb{Z}^d[A]$. This is joint work with J. Thus
 waldner\, "Rational Matrix Digit Systems"\, to appear in "Linear and Multi
 linear Algebra".\n
LOCATION:https://researchseminars.org/talk/OWNS/76/
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