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Enumerative combinatorics, graph theory, order theory, posets, matroids, designs and other discrete structures. It also includes algebraic, analytic and probabilistic combinatorics.
7
votes
Accepted
Neighborhood fingerprint of a graph
The answer is no.
Among Andries E. Brouwer's web pages at TU Eindhoven, the Cages page lists three non-isomorphic graphs on $70$ vertices (they are $(3,10)$-cages, found by O'Keefe & Wong 1980) with …
8
votes
Continued fraction expansion of an algebraic number and its conjugates
A uniform answer for all such cases is going to be too much to expect when $n > 2$.
To begin with, $w$ may not even have a continued fraction expansion - it may fail to be real! (But at least the con …
8
votes
Seeking very regular $\mathbb Q$-acyclic complexes
Here's at least a couple of candidate designs which have the first four properties, although I haven't checked acyclicity and don't yet see how to exploit the existing symmetries to check it other tha …