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3 questions
8
votes
0
answers
226
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A variation of necklace splitting
Our problem is the following:
Let $n$ and $k$ be integers.
We are given two (unclasped) necklaces, each with $n$ colored stones: a top necklace which has $k$ colors and a bottom necklace which has 2 ...
3
votes
1
answer
445
views
Largest symmetric matrix given rank
Let $\mathscr{M}[n,d]$ be collection of $n\times n$ symmetric matrices with real entries from $\{0,1\}$ such that every row/column is distinct with sum of every row/column being $d$.
What is minimum ...
1
vote
0
answers
138
views
Minimum rank of certain matrices
Let $\mathscr{M}[n]$ be collection of $n\times n$ matrices with real entries from $\{0,1\}$ such that every row is distinct and every column is distinct.
What is minimum real rank of matrices in $\...