Reputation
2,442
Next privilege 2,500 Rep.
Create tag synonyms
Badges
2 8 21
Newest
 Student
Impact
~19k people reached

1d
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.
Jan
24
reviewed Approve An equivalence relation on the space of polynomials in one complex variable
Dec
19
reviewed Approve Looking for Uehara, Massey article
Dec
18
reviewed No Action Needed Does the Mandelbrot set have infinite VC dimension?
Dec
15
reviewed Approve Is the modularisation of a unitary fusion category always unitary?
Dec
2
comment Partition regular systems: do they have solution in (very dense) set of integers?
Sean, does this argument come up often in additive combinatorics? I've used it before (to dodge sparse colour classes when proving Ramsey results) but haven't until now seen it elsewhere.
Dec
2
reviewed Approve A question of the book Elements of the representation theory of associative algebras volume 1
Nov
30
comment Maximal induced cycles on $n$-clique graphs
This question would surely be cleaner stated in terms of hypergraphs. You are asking for the longest induced cycle over all $n$-uniform hypergraphs in which every pair of edges shares precisely one vertex. Here induced cycle should mean a (cyclic) sequence of vertices such that each adjacent pair is contained in some edge, and no non-adjacent pairs are contained in any edge.
Nov
30
comment Consecutive integers divisible by consecutive small numbers
@Wolfgang Thank you, that was a particularly silly misreading of the question. I'll delete it to reduce clutter.
Nov
30
reviewed No Action Needed geometric interpretation of derivation between two algebras
Nov
24
reviewed No Action Needed Generators of associated graded algebra
Nov
20
reviewed No Action Needed Can a stochastic Turing machine output a consistent extension of PA with positive probability?
Nov
20
comment Do graphs with $\omega(G) = \chi(G)$ grow “common” as $|V|$ grows large?
Is your notation slightly off? It looks like $\mathcal P_2([n])$ is just the set of pairs from $[n]$. In any case, a random graph has clique number $\log n$ and chromatic number $n/\log n$ (up to constants) with high probability, so $q_n \to 0$.
Nov
20
comment Edge-perspective degree distribution
In other words, a random endpoint of a random edge is not a uniformly random vertex: there is a bias towards the vertices of higher degree. The similar fact that a random neighbour of a random vertex is not a uniformly random vertex leads to the observation that your friends will tend to have more friends than you on average.
Nov
19
reviewed Reject Monte Carlo Simulation - efficient simulation of tail outcomes
Nov
19
comment a property implying co-circularity
Not necessarily: this will hold for any shape with a transitive group of isometries, which includes for example non-square rectangles.
Nov
19
reviewed No Action Needed Minimal solution of simultaneous congruences
Nov
19
revised A natural Lascoux-Schützenberger involutions on plane partitions
merge separate answer
Nov
17
reviewed Looks OK The homology of the braid group with coefficients in the Burau representation