List questions from combinatorics-on-words

356

Views

Does the fraction of distinct substrings in prefixes of the Thue–Morse sequence of length $2^n$ tend to $73/96$?

Published on 25 Mar 2026 - 4:43

171

Views

Find the number of $n$-length Lyndon words on alphabet $\{0,1\}$ with $k$ blocks of 0's.

Published on 24 Apr 2026 - 13:01

70

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How many “words” of any length can be made from the letters in word: MAMMA?

Published on 26 Mar 2026 - 14:23

173

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Word problem and quotient group

Published on 26 Mar 2026 - 7:56

17

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What is the minimal possible length of an $n$-universal word?

Published on 15 Mar 2026 - 19:07

72

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Combinatorial set theory: finding the cardinality of a set

Published on 26 Mar 2026 - 14:24

86

Views

How many length-$k$ ternary strings have evenly many of a given symbol?

Published on 26 Mar 2026 - 17:35

112

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However, how long will it take to randomly generate an $n$-universal word?

Published on 11 Apr 2026 - 11:14

262

Views

Counting with Recurrence Relations

Published on 12 Apr 2026 - 5:53

145

Views

Finding number of words that can be made from four letters if letters can be repeated and one can only be used an odd number of times.

Published on 26 Mar 2026 - 14:22

47

Views

form a string from characters

Published on 26 Mar 2026 - 16:02

151

Views

Random walk on a pentagon touching all vertices

Published on 26 Mar 2026 - 14:20

51

Views

Lists of length $n$ with symbols $\{1, 2, 3, \dots , 12 \}$ where $a_\max-a_\min \leq 5$

Published on 25 Apr 2026 - 12:04

683

Views

Length of a word

Published on 30 Apr 2026 - 14:40

242

Views

Generalized repetitions of letters with limited amount of adjacent letters

Published on 26 Mar 2026 - 14:21

List Question

Does the fraction of distinct substrings in prefixes of the Thue–Morse sequence of length $2^n$ tend to $73/96$?

Find the number of $n$-length Lyndon words on alphabet $\{0,1\}$ with $k$ blocks of 0's.

How many “words” of any length can be made from the letters in word: MAMMA?

Word problem and quotient group

What is the minimal possible length of an $n$-universal word?

Combinatorial set theory: finding the cardinality of a set

How many length-$k$ ternary strings have evenly many of a given symbol?

However, how long will it take to randomly generate an $n$-universal word?

Counting with Recurrence Relations

Finding number of words that can be made from four letters if letters can be repeated and one can only be used an odd number of times.

form a string from characters

Random walk on a pentagon touching all vertices

Lists of length $n$ with symbols $\{1, 2, 3, \dots , 12 \}$ where $a_\max-a_\min \leq 5$

Length of a word

Generalized repetitions of letters with limited amount of adjacent letters

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