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Category Archives: Research
Mathematical Aphorisms. Part 6.
It seems underemphasized that the parsimony of ZFC in the way of ‘types’ (having only one sort called sets) has the following practical and notational virtue: you can get by with a single type of the quantifier , and a … Continue reading
Posted in Category Theory, expository, logic, Olds, Research
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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.) MasbaumVaintrob trees (m.v.t.) Of course, while the latter three … Continue reading
Posted in expository, Higher trees, Mathematics, News, Olds, Research, Simplicial complexes, Structure theory
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Vignettes. Part 12.
Did you know that mathematics will provide you with moreorless standardized tools to usefully express commonlyoccurring 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
Posted in digraph theory, expository, Mathematics, Olds, Research, Technology.
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Compressing and summarizing. Part 3.
[Disclaimer: this a blogpost 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 BangJensen, Stéphane Bessy, Frédéric Havet, Anders Yeo … Continue reading
Compressing and summarizing. Part 2.
[Disclaimer: this a blogpost 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
Posted in compressing and summarizing, Mathematics, News, Research
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Vignettes. Part 5.
Arguably the simplest nontrivial example of an unlabelled simple undirected graph which is not reconstructible from its vertexdeleted subgraphs is the regular tree, illustrated in parts by Needfull to say: that you only see five neighbors at each vertex is … Continue reading
Posted in expository, Higher trees, Mathematics, Olds, Research
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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 umbrellaterm higher trees for object of any reasonable category which admits a reasonable forgetful … Continue reading
Posted in Higher trees, Mathematics, News, Research
Tagged DiestelOumdecompositions
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