Reputation
1,598
Top tag
Next privilege 2,000 Rep.
Edit questions and answers
Badges
7 25
Newest
 Yearling
Impact
~39k people reached

  • 0 posts edited
  • 2 helpful flags
  • 42 votes cast
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