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math.CO2019★ 2 cited
An Optimization-Based Sum-of-Squares Approach to Vizing's Conjecture
Elisabeth Gaar, Daniel Krenn, Susan Margulies +1
Vizing's conjecture (open since 1968) relates the sizes of dominating sets in two graphs to the size of a dominating set in their Cartesian product graph. In this paper, we formula…
math.CO2018
Esthetic Numbers and Lifting Restrictions on the Analysis of Summatory Functions of Regular Sequences
Clemens Heuberger, Daniel Krenn
When asymptotically analysing the summatory function of a -regular sequence in the sense of Allouche and Shallit, the eigenvalues of the sum of matrices of the linear representa…
math.CO2018
Analysis of Summatory Functions of Regular Sequences: Transducer and Pascal's Rhombus
Clemens Heuberger, Daniel Krenn, Helmut Prodinger
The summatory function of a -regular sequence in the sense of Allouche and Shallit is analysed asymptotically. The result is a sum of periodic fluctuations for eigenvalues of ab…