Category Archives: Research

Higher Trees Today. Part 0.

For the time being, the installments of the serial ‘Higher Trees Today’ will focus on three kinds of higher trees: Contractible Spaces of Choices (c.s.c.) Diestel–Oum decompositions (d.o.d.) Kalai trees (k.t.) Masbaum-Vaintrob trees (m.v.t.) Of course, while the latter three … Continue reading

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Vignettes. Part 12.

Did you know that mathematics will provide you with more-or-less standardized tools to usefully express commonly-occurring ideas? For exaple, the following illustration contains at least three examples of this: (0) the symbol for boundaries of things, the symbol to symbolize … Continue reading

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Compressing and summarizing. Part 3.

[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/1707.09400. Compression ratio here is high. ]   This recent preprint of Jørgen Bang-Jensen, Stéphane Bessy, Frédéric Havet, Anders Yeo … Continue reading

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Compressing and summarizing. Part 2.

[Disclaimer: this a blog-post consciously written in the style adumbrated in Compressing and summarizing. Part 0. For the original, see arXiv:1707.09005 [math.LO]. Compression ratio here is high. ] The recent preprint arXiv:1707.09005 of Michael Lieberman, Jiří Rosický, Sebastien Vasey is … Continue reading

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Vignettes. Part 5.

Arguably the simplest non-trivial example of an unlabelled simple undirected graph which is not reconstructible from its vertex-deleted subgraphs is the -regular tree, illustrated in parts by Needfull to say: that you only see five neighbors at each vertex is … Continue reading

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News in higher trees. Part 1.

Trees of all kinds are of fundamental importance. The higher, the hollower, the hallower, the gnarlier, and, most importantly, the livelier they tend to be. I use an umbrella-term higher trees for object of any reasonable category which admits a reasonable forgetful … Continue reading

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Mathematical Aphorisms. Part 0.

In Constructive Mathematics, proof-by-exhaustion is not in general exhaustive, though often still exhausting.

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