All Questions
Tagged with combinatorics-on-words algorithms
8 questions
10
votes
1
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467
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Elegant proof for $xy < yx \Leftrightarrow x^\mathbb{N} < y^\mathbb{N}$
Let $x, y$ be finite words over totally ordered alphabet and $<$ denote the lexicographical order, i.e for two not necessarily finite words we say $x < y$ iff one of the following holds
There ...
- 163
1
vote
0
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169
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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 $x_1 \neq x_2$
In this question, the term “word” implies a binary word, i.e. a sequence of bits.
Let $W(x)$ denote the number of non-zero bits in a word $x$.
Assuming that $x$ is an $s$-bit word and $0 \le k < s$,...
- 959
2
votes
1
answer
168
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Is there an efficient algorithm that allows to construct a binary word with particular properties related to its horizontal and vertical “subwords”?
Let $w$ denote an $mn$-bit word (i.e. a binary word of length $mn$). Assuming that $b_{i,j}$ denote individual bits, we can represent $w$ in the “rectangular” form as follows:
$$\begin{array}{l}
b_{1....
- 959
1
vote
1
answer
121
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Is there an efficient generalized algorithm to generate a set of binary words satisfying a particular cross-correlation property?
In this question, the term “word” implies a binary word, i.e. a sequence of bits.
Let $W(w)$ denote the number of non-zero bits in a word $w$.
Assuming that $l \geq 2$ is even, an $l$-bit word $w$ is ...
- 959
7
votes
2
answers
319
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Is there an efficient generalized algorithm to find at least one binary word with the maximum rotational imbalance and the full $\{0, 1\}$-balance?
Assuming that $x$ is a sequence of $l$ bits (i.e. a binary word of length $l$) and $0 \le m < l$, let $R(x, m)$ denote the result of the left bitwise rotation (i.e. the left circular shift) of $x$ ...
- 959
5
votes
1
answer
123
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Algorithms to factorize words into product of powers
I came across this problem, which I guess is well known to combinatorialists of words, so I write here to see if someone can help me with some references.
Let $A$ be a finite set of symbols, are there ...
- 477
0
votes
1
answer
159
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How many words are there such that some word $X$ is subsequence of them?
Let's define subsequence of the word as part of the word created by deleting some of its letters, for example aetics is a subsequence of mathematics.
QUESTION.
Given a $3$-letter word (let's call it ...
5
votes
1
answer
447
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Periodic strings
I wish to ask a problem in periodic strings, it might be well-known but I am a beginner in this subject, so I am very glad if someones can show me. My problem is that can we add some string to the end ...
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