Ben Barber
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 2d reviewed Reviewed Choosing two-colorable subgraph in a triangulation 2d revised Choosing two-colorable subgraph in a triangulation top-level tag Apr 26 reviewed No Action Needed Are these two difference scheme of the same differential equation equivalent? Apr 26 comment maximal sets of vertices that avoids a clique There is an obvious generalisation of the maximal independent set algorithm to maximal triangle-free sets: maintain the same three lists of vertices that are in, might be in and you have decided are not in, and update based on the formation of triangles rather than the presence of edges. Apr 26 comment chromatic polynomial of G - Join graph On the terminology question, what you have done is "blow up each vertex $i$ to a clique of order $m_i$". Apr 22 reviewed Looks OK Are braid groups conjugacy separable? Apr 21 reviewed Approve Law of Large Numbers for Martingales Apr 18 reviewed Reviewed Rectifiable currents Apr 17 comment Sets of points containing permutations - a Ramsey-type question @LászlóKozma, please do post an answer if you'd like to explain the connection. Apr 11 comment Growth of inner products between two random vectors on the sparse hypercube What ranges of $s$ and $d$ are of interest? If say $s$ is some constant fraction of $d$ then the inner products are tightly concentrated in an interval of length $O(\sqrt d)$ around $0$. More generally, the inner products look like taking some number of steps of the symmetric random walk on $\mathbb Z$, with varying degrees of laziness. Apr 4 answered Representing a graph's vertices as linear combinations of paths Mar 22 comment Perfect matchings that never combine to form cycle union cover If single edges do not count as cycles of length $2$ then this can be cheated out by taking a complete bipartite graph and a single vertex-disjoint edge. If single edges do count as cycles of length $2$ then every union of two perfect matchings is a union of cycles that cover the vertex set. Mar 17 reviewed No Action Needed $L^\infty-L^2$ smoothing for heat equation on manifold using Nash-Moser-De-Giorgi technique Mar 11 comment One more strengthening of Frankl's conjecture I was going to mention the current Polymath project hosted on Gowers's blog, but I see from your previous question that you already know about it. You might find a higher concentration of people able to answer your question there. Mar 9 reviewed Reject Question about the stochastic integral of martingales Feb 26 comment Infinite graph with degrees given If my quick translation between your question and the notation from the paper is correct, the answer is in fact yes, and the graph can be taken to be a forest. Feb 26 answered Infinite graph with degrees given Feb 24 reviewed No Action Needed Complex Structure Moduli of Elliptic Fibrations Feb 11 reviewed Approve Can you simplify (or approximate) $\sum_{n=0}^{N-1} \binom{N-1}n \frac{(-1)^n}{n+1} e^{-\frac{n}{2(n+1)}\lambda}$? Feb 4 comment Probability bound for perfect matching The answer to your previous question notes that $p = \log n / n$ is a sharp threshold for the existence of a perfect matching. This means that, in order to get probabilities for the existence of a perfect matching that are distinguishable from $0$ or $1$, you have to choose $p$ incredibly carefully with respect to $n$. You might find more precise estimates of the threshold with searches including the phrase "critical window", but that's unlikely to tell you much about the exact probability that a perfect matching exists.