### 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 $$0 \leq y_1 \leq m-3$$.