Abstract
We prove some particular cases of the following conjecture of Perrin and Schützenberger, known as “the triangle conjecture.” Let A = { a, b} be a two-letter alphabet, d a positive integer and let B d = { a i ba j | 0 ⩽ i + j ⩽ d}. If X ⊂ B d is a code, then | X| ⩽ d + 1.
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