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Compressing and summarizing. Part 4.
[Disclaimer: this a blogpost consciously written in the style adumbrated in Compressing and summarizing. Part 0. For the original, see https://arxiv.org/abs/1708.00148. Compression ratio here is high. ] This reports on this recent preprint by Siddharth Baskar and Alex Kruckman. Loc. … Continue reading
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Compressing and summarizing. Part 1.
Disclaimer: this a blogpost consciously written in the style adumbrated in Compressing and summarizing. Part 0. For the original, see Historia Mathematica Volume 6, Issue 3, August 1979, Pages 294304. For brevity, the source is referenced by loc. cit., and … Continue reading
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Mathematical Aphorisms. Part 2.
One should intentionally take an intensional view on the things one cares about.
Visualizing graphs, for small graphs, in contexts in which graphs are thought of as twouniform hypergraphs.
For reasonably small graphs, it can make for beautiful and usefullyselfexplanatory illustrations to visualize graphs by diaphanous rodlike shapes overlapping where the vertices are supposed to be. In particular, the vertex degrees thus become implicitly visualized via the darkness of the … Continue reading
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Vignettes. Part 3.
A usual convention in topology is to have arc mean path in a space which also is a homeomorphism onto its image. This is simultaneously a felicity and a hazardousness infelicity. It is a hazardousness in that in combinatorics it … Continue reading
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Vignettes. Part 2.
Mathematicians working in algebraic graph theory call what mathematicians working in graphtheory independent sets by the name cocliques, and call complete graphs by the name cliques. Mathematicians working in category theory tend to call those independent sets by the name free … Continue reading
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The rank and the kernel of a rayless tree
To prove Proposition 1.2 in the previous post on branches, we will furthermore work with the notion of rank of a rayless tree, i.e., a rankfunction mapping any rayless tree to an ordinal number. For every rayless tree we define … Continue reading
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