Vincent Tjeng
Reputation
1,598
Top tag
Next privilege 2,000 Rep.
 2d comment Making Friends around a Circular Table I think that the swaps I have up there are far from optimal - thanks for showing that the bound can be pushed down slightly. Dec 8 awarded Yearling Oct 26 awarded Popular Question Oct 25 comment Making Friends around a Circular Table @hlapointe $f(n)$ refers to the number of switches you need when you can only switch people who are sitting next to each other, and $g(n)$ to the number of switches you need when you can switch any pair of people. For a given value of $n$, we would expect $f(n) \ge g(n)$ Oct 25 awarded Favorite Question Oct 12 awarded Popular Question Oct 3 awarded Enlightened Oct 3 awarded Nice Answer Mar 3 awarded Popular Question Feb 17 asked Under what conditions is $AA^T$ invertible? Jan 17 comment List of non-immediately-repeating permutations By the way - 36.7% is approximately $\frac{1}{e}$, and I'm sure there's a reason why! Dec 26 comment Making Friends around a Circular Table @Daugmented by permuting the people, do you mean to select a subset of the people and to rotate their position on the table while keeping the rest of the people fixed (and thus switching is a special case of permutation with sets of 2?) Dec 16 awarded Good Question Dec 9 awarded Caucus Dec 8 revised Number of Secret Santa directed graph with a largest cycle of given size edited tags Dec 8 asked Number of Secret Santa directed graph with a largest cycle of given size Dec 8 awarded Yearling Nov 25 comment Making Friends around a Circular Table @user170039 sorry for the delay. If I understand your solution correctly, you're suggesting that you can think of $n$ people making friends with each other in $g(n)$ time, and then inserting the $(n+1)$-th person who can get to know everyone in $\lceil (n+1)/2 \rceil$. I don't think that this is correct, since you cannot simply ignore the $(n+1)$-th person: even if he sat on the table and did not move, he would affect the friendships that are formed on the table (since you only make friends with people you sit directly next to). Nov 4 comment Making Friends around a Circular Table @user170039 do you mind elaborating how you got to that bound, or was it just a conjecture? Aug 27 awarded Popular Question