bio | website | |
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visits | member for | 7 months |
seen | Apr 16 at 21:45 | |
stats | profile views | 100 |
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 0000001111,0000111111,0001101100,0011100011,0011111000,0100111010,0110001001,0111001110,1000010000,1001100111,1100011100,1101000110,1110000011,1111100000,1111111000 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. |