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4h
reviewed No Action Needed Eigenvectors of symmetric positive semidefinite matrices as measurable functions
23h
reviewed No Action Needed What is an upper bound for $|E(X|\mathcal{A})-E(X)|$?
2d
reviewed No Action Needed Smoothness of Value function for SDE with discontinuous coefficients
2d
reviewed No Action Needed Equivalent ways to study a semilinear parabolic equation as a perturbed abstract Cauchy problem
May
1
answered Is there a subset of $\Sigma_n$ s.t. each pair of elements is once in each pair of positions?
May
1
comment Is there a subset of $\Sigma_n$ s.t. each pair of elements is once in each pair of positions?
Technically, the question asks for a sharply $2$-transitive set, not group. I'm not aware of an example that is a set but not a group, but see arxiv.org/pdf/1604.04429v1.pdf for an example of a sharply $6$-transitive set on 13 points which is not a group.
May
1
reviewed No Action Needed Unit-Distance Polyhedra
Apr
29
comment Which graphs embedded in surfaces have symmetries acting transitively on vertex-edge flags?
The only other option is that the arc-stabiliser is trivial and hence the group acts regularly on arcs. In that case, the vertex-stabiliser acts regularly on the neighbours, so it must be either cyclic of order $k$, or dihedral of order $k$ (in which case $k$ is even). These are all quite well studied objects, although not as much as the regular ones. In particular, they can be defined group-theoretically and, using this, can be enumerated up to a few thousand vertices and quite high genus, 100 say. (See math.auckland.ac.nz/~conder for example)
Apr
29
comment Which graphs embedded in surfaces have symmetries acting transitively on vertex-edge flags?
A very common term for a vertex-edge flag is an arc. Let me use this for simplicity. You are asking about maps with an arc-transitive group of automorphisms. It's not hard to see that the maximal amount of symmetry a map can have is to be arc-transitive with the arc-stabiliser having order $2$. This is the so-called "regular" case that Noam mentioned. In that case, the vertex-stabiliser is dihedral, of order $2k$, where $k$ is the valency.
Apr
28
reviewed Reviewed How to make Markov Chain model from sequence of data using MATLAB?
Apr
28
comment Constructing the largest finite group with a fixed number of conjugacy classes
The groups are known up to $k=14$ at least, see Vera-López, A., Sangroniz, Josu, The finite groups with thirteen and fourteen conjugacy classes. Math. Nachr. 280 (2007), no. 5-6, 676–694.
Apr
21
reviewed No Action Needed Sum of the dimensions of the rational irreducible representations of $S_k \times S_j$
Apr
21
reviewed No Action Needed Vorticity form of Euler equation: What about harmonic part?
Apr
21
reviewed No Action Needed Decreasing the binding number of an open book while increasing the genus of the pages
Apr
20
comment A question about (unicity of certain cycles in a Cayley graph of a) symmetric group
In other words, you are asking if, in the cubic Cayley graph on $S_n$ with the generators you have given, there is another path of length $2n-4$ between the identity and $(1,n,n-1,\ldots,3)$ besides the one you give...
Apr
18
reviewed No Action Needed Zero knowledge proof of equality
Apr
16
comment Is there a characterization of CI-groups of order less than 100?
I saw a talk about this recently, and there are certainly some open cases of order less than $100$. On the other hand, it is easy to find the answer by brute-force (by computer) up to order $50$ or $60$ or so. In particular, $30$ is certainly "known". (In the sense that some people know the answer, although it might not be in the literature.)
Apr
15
comment Transitive permutation groups which all of their proper subgroups are intransitive
@YCor, if you mean what is the smallest degree of a transitive group with no regular subgroup, it is 6. There are five examples of degree $6$, including for example $A_6$ and (the smallest, by order) $A_4$ on 6 points. The smallest example of prime-power degree has order $32$ and degree $8$.
Apr
14
comment Finite graph colorings without symmetries
First, I'd like to emphasise that the colouring above is not necessarily proper (adjacent vertices may have the same color), but that is what you asked for. (In fact, if you insist on a proper coloring, then the complete bipartite graphs shows that you need at least $2k$ colors.) As for needing only $2$ colors for most graphs, I'm far from an expert on this, but if you search for papers about "distinguishing number", you'll find that more than half of them deal with exactly this question: showing that, in many families of graphs, all but very few have distinguishing number $2$.
Apr
13
revised Finite graph colorings without symmetries
added 34 characters in body