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seen Apr 16 at 21:45

Apr
15
comment What is $\lim_{n\to\infty} \displaystyle \sum_{k=0}^{\lfloor n/2 \rfloor} \binom{n}{2k}\left(4^{-k}\binom{2k}{k}\right)^{\frac{2n}{\log_2{n}}}\,?$
Can I ask my question again in that case? Is the OP right that convergence depends on the constant in the exponent?
Apr
13
comment What is $\lim_{n\to\infty} \displaystyle \sum_{k=0}^{\lfloor n/2 \rfloor} \binom{n}{2k}\left(4^{-k}\binom{2k}{k}\right)^{\frac{2n}{\log_2{n}}}\,?$
Is the OP right that convergence depends on the constant in the exponent? I can't immediately tell from your answer.
Apr
12
comment Probability all inner products are zero
@DouglasZare If the indicator variable $I_i$ is $1$ if the $i$th inner product is $0$, can you tell if the $I_i$ are positively or negatively associated?
Apr
4
awarded  Investor
Feb
15
accepted Smallest non-zero eigenvalue of a (0,1) matrix
Feb
15
comment Smallest non-zero eigenvalue of a (0,1) matrix
There is nothing better than an explicit construction. Thank you. Although it would be great if I could accept the upper and lower bounds answers together.
Feb
14
awarded  Nice Question
Feb
13
asked Smallest non-zero eigenvalue of a (0,1) matrix
Jan
28
awarded  Scholar
Jan
28
accepted Expected maximum inner product
Jan
28
revised Expected maximum inner product
deleted 3 characters in body
Jan
28
comment Expected maximum inner product
Thank you. Is there a matching lower bound which tells me that it is exponentially unlikely to take values smaller than anything just a tiny bit smaller than $\sqrt{m}$ too?
Jan
28
asked Expected maximum inner product
Jan
26
comment Probability a random Toeplitz matrix is singular
@Suvrit Can you give any more details?
Oct
15
awarded  Caucus
Oct
3
comment Puzzle on deleting k bits from binary vectors of length 3k
I have reformulated the problem as a "hitting set" problem and then coded that as a Mixed Integer Linear Program (MILP). I am using some software called Gurobi to solve the MILP. Unfortunately a disadvantage of my method is that I don't have any sense either for how rare it is or if one could do better. My encoding is also naive making it probably very wasteful.
Oct
2
comment Puzzle on deleting k bits from binary vectors of length 3k
I managed to get a $17$ solution for $(15,5)$. They are 0000001111,0000111111,0001101100,0011100011,0011111000,0100111010,0110001‌001,01‌​11001110,1000010000,1001100111,1100011100,1101000110,1110000011,1111‌100000,11111‌​11000 plus the all 0s and all 1s.
Oct
2
awarded  Commentator
Oct
2
revised Puzzle on deleting k bits from binary vectors of length 3k
edited body
Sep
29
comment Puzzle on deleting k bits from binary vectors of length 3k
@Thomas These are the 31 vectors I get from my code for $(10,2)$ 00000000,00000011,00000101,00000110,00001100,00011000,00011111,00110000,00110111‌​,00111011,00111100,01001111,01100000,01100111,01110011,01111000,10001111,10010001‌​,10010010,10101001,10101010,11000000,11000111,11011011,11011100,11100011,11101100‌​,11110000,11111101,11111110,11111111 . On the other question, when I said symmetry I simply meant under the assumption that every vector in a solution appears with its complement.