Michael Lugo's user avatar
Michael Lugo's user avatar
Michael Lugo's user avatar
Michael Lugo
  • Member for 14 years, 5 months
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26 votes
4 answers
2k views

What relationship, if any, is there between the diameter of the Cayley graph and the average distance between group elements?

3 votes
1 answer
1k views

Sprague-Grundy sequence for the ruler game

3 votes
1 answer
3k views

The game of "nimble" with no stacking

14 votes
1 answer
923 views

How many pairs (M, N) of sets of size n have M + N = {0, 1, ..., n^2-1}?

6 votes
2 answers
471 views

Limit law for the number of local maxima in a square lattice of IID random variables

7 votes
4 answers
995 views

Reference for the expected number of prime factors of n larger than n^alpha is -log alpha

18 votes
1 answer
844 views

What's the probability that k + n^2 is squarefree, for fixed k?

36 votes
2 answers
1k views

Is there a combinatorial reason that the (-1)st Catalan number is -1/2?

6 votes
5 answers
2k views

Asymptotic series for roots of polynomials

8 votes
4 answers
2k views

An integral that somehow equals pi^2/6 and involves dilogarithms?

5 votes
2 answers
477 views

Asymptotics of iterated polynomials

36 votes
6 answers
2k views

When are some products of gamma functions algebraic numbers?

10 votes
3 answers
2k views

Is there a Faa di Bruno-like formula for composition of three functions?

66 votes
8 answers
12k views

Why are powers of $\exp(\pi\sqrt{163})$ almost integers?

23 votes
4 answers
9k views

Is there a simple way to compute the number of ways to write a positive integer as the sum of three squares?

19 votes
9 answers
3k views

How can I generate random permutations of [n] with k cycles, where k is much larger than log n?

89 votes
13 answers
141k views

If you break a stick at two points chosen uniformly, the probability the three resulting sticks form a triangle is 1/4. Is there a nice proof of this?

10 votes
4 answers
933 views

What m minimizes E(|m-X|^3) for a random variable X?

80 votes
8 answers
19k views

Teaching statements for math jobs?