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lyrically wicked's user avatar
lyrically wicked
  • Member for 6 years, 8 months
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asked
A non-trivial (not a concatenation of de Bruijn sequences) infinite binary sequence whose initial $2^{n+1}$ bits contain all $n$-bit words for any $n$
revised
A function $g : \{0,1\}^m \to \{0,1\}^{4m}$ such that the “circular discrepancy” between $g(x_1)$ and $g(x_2)$ is $\geq m$ for any $x_1 \neq x_2$
edited title
revised
A function $g : \{0,1\}^m \to \{0,1\}^{4m}$ such that the “circular discrepancy” between $g(x_1)$ and $g(x_2)$ is $\geq m$ for any $x_1 \neq x_2$
edited title
revised
A function $g : \{0,1\}^m \to \{0,1\}^{4m}$ such that the “circular discrepancy” between $g(x_1)$ and $g(x_2)$ is $\geq m$ for any $x_1 \neq x_2$
edited title
revised
A function $g : \{0,1\}^m \to \{0,1\}^{4m}$ such that the “circular discrepancy” between $g(x_1)$ and $g(x_2)$ is $\geq m$ for any $x_1 \neq x_2$
added 53 characters in body
revised
A function $g : \{0,1\}^m \to \{0,1\}^{4m}$ such that the “circular discrepancy” between $g(x_1)$ and $g(x_2)$ is $\geq m$ for any $x_1 \neq x_2$
added 53 characters in body
revised
A function $g : \{0,1\}^m \to \{0,1\}^{4m}$ such that the “circular discrepancy” between $g(x_1)$ and $g(x_2)$ is $\geq m$ for any $x_1 \neq x_2$
added 10 characters in body
revised
A function $g : \{0,1\}^m \to \{0,1\}^{4m}$ such that the “circular discrepancy” between $g(x_1)$ and $g(x_2)$ is $\geq m$ for any $x_1 \neq x_2$
deleted 8 characters in body
revised
A function $g : \{0,1\}^m \to \{0,1\}^{4m}$ such that the “circular discrepancy” between $g(x_1)$ and $g(x_2)$ is $\geq m$ for any $x_1 \neq x_2$
edited body
asked
A function $g : \{0,1\}^m \to \{0,1\}^{4m}$ such that the “circular discrepancy” between $g(x_1)$ and $g(x_2)$ is $\geq m$ for any $x_1 \neq x_2$
accepted
Gaps in the ordinals writable by Ordinal Turing Machines with a single countable parameter
asked
Gaps in the ordinals writable by Ordinal Turing Machines with a single countable parameter
comment
Is there an efficient algorithm that allows to construct a binary word with particular properties related to its horizontal and vertical “subwords”?
In the given $16 \times 16$ matrix the $i$-th row (horizontal subword) is equal to the $i$-th column (vertical subword), which contradicts Property #3.
comment
Is there an efficient algorithm that allows to construct a binary word with particular properties related to its horizontal and vertical “subwords”?
@PeterTaylor: yes, if $m=8, n=8$, we have $\binom{8}{4}=70$ (the number of possible options for a horizontal/vertical $8$-bit subword), which is significantly greater than $m + n = 16$ (the number of all subwords, horizontal and vertical), so it would be reasonable to assume that $W_{64}$ exists.
revised
Is there an efficient algorithm that allows to construct a binary word with particular properties related to its horizontal and vertical “subwords”?
deleted 285 characters in body
comment
Is there an efficient algorithm that allows to construct a binary word with particular properties related to its horizontal and vertical “subwords”?
@PeterTaylor: thank you. I wonder whether it is possible to estimate the number of such words in the set of all $k$-bit words...
asked
Is there an efficient algorithm that allows to construct a binary word with particular properties related to its horizontal and vertical “subwords”?
awarded
 Yearling
accepted
What is the meaning of $\alpha^{+L}$ for $\alpha$ an infinite countable ordinal?
revised
What is the meaning of $\alpha^{+L}$ for $\alpha$ an infinite countable ordinal?
deleted 15 characters in body; edited title
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