Category Archives: Uncategorized

Compressing and summarizing. Part 4.

[Disclaimer: this a blog-post 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 blog-post 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 294-304. 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.

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Visualizing graphs, for small graphs, in contexts in which graphs are thought of as two-uniform hypergraphs.

For reasonably small graphs, it can make for beautiful and usefully-self-explanatory illustrations to visualize graphs by diaphanous rod-like 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  graph-theory 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 rank-function mapping any rayless tree to an ordinal number. For every rayless tree we define … Continue reading

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