Unavoidable Sets

Let \(X = \{a{\diamond}^{m-2}a,a{\diamond}^{m-2}c,b{\diamond}^{m-2}b,c{\diamond}^{m-2}c, a{\diamond}^{x_1}b{\diamond}^{x_2}b, b{\diamond}^{y_1}b{\diamond}^{y_2}c \} \) be an \(m\)-uniform set. The avoidability of sets of this form has implications on the minimum number of holes in unavoidable \(m\)-uniform sets of partial words over a \(k\)-letter alphabet. This applet takes values of \(m\), \(x_1\), and \(y_1\) and finds a list of periods of infinite words that avoid \(X\). To input \(m\), \(x_1\), and \(y_1\), type the numbers in the text box separated by a comma and a space (e.g. \(10,\;6,\;2\;\)). Note that \(m \geq 3\), \(0 \leq x_1 \leq m-3\), and \(0 \leq y_1 \leq m-3\).

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