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cs.DM2024
Kolmogorov complexity as a combinatorial tool
Alexander Shen
Kolmogorov complexity is often used as a convenient language for counting and/or probabilistic existence proofs. However, there are some applications where Kolmogorov complexity is…
math.HO2024
Comparing angles in Euclid's Elements
Alexander Shen
The exposition in Euclid's Elements contains an obvious gap (seemingly unnoticed by most commentators): he often compares not just angles, but *groups* of angles, and at the same t…
cs.IT2024
Conditional normality and finite-state dimensions revisited
Alexander Shen
The notion of a normal bit sequence was introduced by Borel in 1909; it was the first definition of an individual random object. Normality is a weak notion of randomness requiring…