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This can be proved by constructing a square-free word without the two-letter combination ab. As a result, bcba cbca cbaca is the longest square-free word without the combination ab and its length is equal to 13. Note that over a more than three-letter alphabet there are square-free words of any length without an arbitrary two-letter combination.
initialism = an abbreviation pronounced wholly or partly using the names of its constituent letters, e.g., CD = compact disc, pronounced cee dee; pseudo-blend = an abbreviation whose extra or omitted letters mean that it cannot stand as a true acronym, initialism, or portmanteau (a word formed by combining two or more words).
The theorem can be used in analytic combinatorics to estimate the number of words of length n generated by a given unambiguous context-free grammar, as n grows large. The following example is given by Gruber, Lee & Shallit (2012): the unambiguous context-free grammar G over the alphabet {0,1} has start symbol S and the following rules
Scrabble is a word game in which two to four players score points by placing tiles, each bearing a single letter, onto a game board divided into a 15×15 grid of squares. The tiles must form words that, in crossword fashion, read left to right in rows or downward in columns and are included in a standard dictionary or lexicon.
[2] The original word or phrase is known as the subject of the anagram. Any word or phrase that exactly reproduces the letters in another order is an anagram. Someone who creates anagrams may be called an "anagrammatist", [3] and the goal of a serious or skilled anagrammatist is to produce anagrams that reflect or comment on their subject.
The two letters of the digram are considered opposite corners of a rectangle in the key table. To perform the substitution, apply the following 4 rules, in order, to each pair of letters in the plaintext: If both letters are the same (or only one letter is left), add an "X" after the first letter. Encrypt the new pair and continue.
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Combinatorics on words is a fairly new field of mathematics, branching from combinatorics, which focuses on the study of words and formal languages. The subject looks at letters or symbols, and the sequences they form. Combinatorics on words affects various areas of mathematical study, including algebra and computer science. There have been a ...