375 reputation
111
bio website
location Germany
age 31
visits member for 2 years, 1 month
seen Feb 14 at 13:12

work: mathematics (operations research), web development (Rails) other interests: sports (running, bodyweight exercises), game theory


Jun
8
revised What is the use of the Dot Product of two vectors?
added 13 characters in body; deleted 1 characters in body
Jun
8
awarded  Teacher
Jun
8
answered What is the use of the Dot Product of two vectors?
Jun
8
comment Game Theory: Is there an “unexploitable” strategy in No Limit Holdem?
Note I said "non-negative", not "positive". So if all players apply the same strategy, the expected payoff for everyone would be zero, which is non-negative.
Jun
8
asked Game Theory: Is there an “unexploitable” strategy in No Limit Holdem?
Mar
29
comment Cocktail bar problem
@Aryabhata: Of course $\frac{n-1}{2}$ are not enough, but using the construction of the book one can obtain $\frac{n+1}{2}$ paths that satisfy our requirements.
Mar
29
comment Cocktail bar problem
Ok the construction described in the book works as well for the case of $n$ being odd, for which it yields $\frac{n+1}{2}$ paths where the $\frac{n-1}{2}$ pairs $\{1,n\},\{2,n-1\},\dots$ are covered exactly twice, all others being covered exactly once.
Mar
29
comment Cocktail bar problem
very nice approach, thanks!
Mar
29
accepted Cocktail bar problem
Mar
29
comment Cocktail bar problem
I understand the proof for the case of $n$ being even, and it is indeed the minimum as $|A|\geq \frac{n}{2}$ which Greg Martin pointed out in his answer. But in case of $n$ being odd, we need at least $\frac{n+1}{2}$ paths, and I don't see how to construct them from the $\frac{n-1}{2}$ cycles. Am I missing something trivial?
Mar
29
comment Cocktail bar problem
@hardmath: I'm not looking for the number of swaps that have to be made, I'm only interested in $A$ or its cardinality. I reformulated the question in order to make it more clear what I mean.
Mar
29
revised Cocktail bar problem
made question formulation more precise
Mar
28
awarded  Yearling
Mar
28
asked Cocktail bar problem
Mar
13
revised What is the order of $2$ in $(\mathbb{Z}/n\mathbb{Z})^\times$?
edited title
Mar
13
awarded  Scholar
Mar
13
accepted What is the order of $2$ in $(\mathbb{Z}/n\mathbb{Z})^\times$?
Mar
12
awarded  Supporter
Mar
12
awarded  Nice Question
Mar
11
asked What is the order of $2$ in $(\mathbb{Z}/n\mathbb{Z})^\times$?