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Sökning: AMNE:(NATURVETENSKAP Matematik Diskret matematik) > Konferensbidrag

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  • Uscka-Wehlou, Hanna, 1973- (författare)
  • A Run-hierarchical Description of Upper Mechanical Words with Irrational Slopes Using Continued Fractions
  • 2008
  • Ingår i: Proceedings of the 12th Mons Theoretical Science Days, Mons, Belgium 27-30 August 2008. - Mons, Belgium : Mons University.
  • Konferensbidrag (refereegranskat)abstract
    • The main result is a run-hierarchical description (by continued fractions) of upper mechanical words with positive irrational slope less than 1 and intercept 0. We compare this description with two classical methods of forming of such words. In order to be able to perform the comparison, we present a quantitative analysis of our method. We use the denominator of the convergents of the continued fraction expansion of the slope to compute the length of the prefixes obtained by our method. Due to the special treatment which is given to the elements equal to 1, our method gives in some cases longer prefixes than the two other methods. Our method reflects the hierarchy of runs, by analogy to digital lines, which can give a new understanding of the construction of upper mechanical words.
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  • Uscka-Wehlou, Hanna, 1973- (författare)
  • Continued fractions and digital lines with irrational slopes
  • 2008
  • Ingår i: Proceedings of DGCI, the 14th International Conference on DISCRETE GEOMETRY for COMPUTER IMAGERY. DGCI 2008. - Berlin Heidelberg : Springer-Verlag. - 9783540791256 ; , s. 93-104
  • Konferensbidrag (refereegranskat)abstract
    • This paper expands on previous work on relationships between digital linesand continued fractions (CF). The main result is a parsimonious description of the construction of the digital line based only on the elements of the CF representing its slope and containing only simple integer computations. The description reflects the hierarchy of digitization runs, which raises the possibility of dividing digital lines into equivalence classes depending on the CF expansions of their slopes. Our work is confined to irrational slopes since, to our knowledge, there exists no such description for these,  in contrast to rational slopes which have been extensively examined. The description is exact and does not use approximations by rationals. Examples of lines withirrational slopes and with very simple digitization patterns are presented. These include both slopes with periodic and non-periodic CF expansions, i.e.\ both quadratic surds and other irrationals.
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  • Uscka-Wehlou, Hanna, 1973- (författare)
  • Sturmian words with balanced construction
  • 2009
  • Ingår i: Proceedings of Words 2009, the 7th International Conference on Words           (Salerno, Italy), 14--18 September 2009. - Italy : Salerno University.
  • Konferensbidrag (refereegranskat)abstract
    • In this paper we define Sturmian words with balanced construction. We formulate a fixed-point theorem for Sturmian words and analyze the set of all fixed points. The inspiration for this work came from the Kolakoski word and the general idea of self-reading sequences by P\u{a}un and Salomaa. The basis for this article is the author's earlier research on the influence of the continued fraction elements in the expansion of a positive irrational slope $a<1$ on the construction of runs for the upper mechanical word with slope $a$and intercept $0$.
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  • Hellström, Lars, 1974- (författare)
  • Critical Pairs in Network Rewriting
  • 2014
  • Ingår i: IWC 2014. ; , s. 9-13
  • Konferensbidrag (refereegranskat)abstract
    • This extended abstract breifly introduces rewriting of networks (directed acyclic graphs with the extra structure needed to serve as expressions for PROducts and Permutations categories) and describes the critical pairs aspects of this theory. The author's interest in these comes from wanting to do equational reasoning in algebraic theories (such as Hopf algebras) that mix ordinary operations with co-operations; networks then serve as a formalism for expressions.The main message is to point out two phenomena that arise in network rewriting. The first is that of non-convexity of rules, wherein the left hand side of a rule need not be syntactically similar to a symbol in any extension of the underlying signature. The second is one of critical pairs potentially arising where two redexes wrap around each other even when they do not intersect.
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  • Freij-Hollanti, Ragnar, et al. (författare)
  • Matroid Theory via Examples
  • 2016
  • Ingår i: International Zurich Seminar on Communications - Proceedings. ; , s. 45-49
  • Konferensbidrag (refereegranskat)
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