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Aug
20
comment Important formulas in Combinatorics
The question says, "2) Present the formula explicitly (not just by name or by a link or reference)." You don't have to make it complete, but if you are going to start an answer you should be willing to write out the first example with an appropriately self-contained description, as others have been doing and as the question asks.
Aug
19
comment Important formulas in Combinatorics
Please make this self-contained by including explicit uses of the formula, as the question requests.
Aug
19
comment Important formulas in Combinatorics
Please make this self-contained by including explicit uses of the formula, as the question requests.
Aug
19
comment Important formulas in Combinatorics
Please make this self-contained by including explicit uses of the formula, as the question requests.
Aug
18
awarded  Nice Answer
Aug
15
comment set of centers of sphere inscribed in tetrahedron
Why restrict $A$, $B$, and $C$ to be on the sphere?
Aug
15
comment Set of balls which the number of the ball intersects lines on the plane is bounded
Even if you don't like the answer that was given before, you should still link to the other question. This avoids duplication of effort. It lets people read the discussion of the earlier version, where you clarified, for example, that you mean closed balls.
Aug
11
reviewed Approve Maximal Number of Pairs of Orthogonal vectors in a set of $n$ vectors in $\mathbb{R}^3$
Aug
10
comment Diameter of the modified bubble-sort graph
You can show that a typical permutation is of distance at least $cn^2$ from the identity by considering the average of the number of inversions of $(1 2 ... n)^k$ times the permutation. However, this leads to the wrong constant.
Aug
8
awarded  Nice Answer
Aug
6
awarded  Nice Answer
Jul
27
comment Determining whether $k(x + x^{-1})$ is post-critically finite for $0 < |k| < 1$
How is $2k-1$ greater than $1$ in absolute value? Is $k$ negative or complex, or do you mean a non-Archimedean absolute value $\alpha ^ {v(\cdot)}$?
Jul
27
comment Randomly partitioning the unit interval with continuous functions
Do you want continuous functions or piecewise constant functions? Why do you use $w$ and not $1/n$?
Jul
15
awarded  Enlightened
Jul
15
awarded  Nice Answer
Jul
8
comment Recursive sequence of binomial random variables
The right tail bounds seem much easier than the left tail bounds. For example, Markov's inequality says $P[X_k > (1+p+\epsilon)^k] \le (\frac{1+p}{1+p+\epsilon})^k$.
Jul
4
reviewed Approve How many labelled disconnected simple graphs have n vertices and floor((n choose 2)/2) edges?
Jul
1
answered Given $x$ in a path-connected open set $S$ on the plane, are there non-crossing paths from $x$ to every point in $\partial S$?
Jul
1
comment Given $x$ in a path-connected open set $S$ on the plane, are there non-crossing paths from $x$ to every point in $\partial S$?
Your argument using the Riemann mapping theorem is flawed. The Riemann map is not guaranteed to extend continuously to the boundary. See Carathéodory's theorem.
Jun
29
revised Probability that random nonnegative integer matrix is singular
Switched matrices. Added OEIS information.