Category Archives: Higher trees

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

Posted in expository, Higher trees, Mathematics, News, Olds, Research, Silviculture, Simplicial complexes, Structure theory | Leave a comment

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

Posted in expository, Higher trees, Mathematics, Olds, Research | Leave a comment

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

Posted in Higher trees, Mathematics, News, Research | Tagged | Leave a comment

News in higher trees. Part 0.

Tree-like structures are of fundamental importance. Not least because of the important principle of independence of arbitrary choices up to a contractible space of choices which is ubiquitous in modern mathematics.  Higher trees are close to my heart for more … Continue reading

Posted in gnarliness, Higher trees, Kalai trees, Mathematics, News, Research, Simplicial complexes | Leave a comment