Shadows under the word-subword relation

Quite surprisingly, it seems that the minimal shadow problem for the word-subword relation introduced here has not been studied before, whereas its analogs for sets [1–4], sequences [5], and vector spaces over finite fields [6] are well known. For an alphabet X = {0, 1, . . . , q − 1}, we consider the set X k of words xk = x1x2 . . . xk of length k. For a word ak = a1a2 . . . ak ∈ X k, we define its left shadow shad(a) = a2 . . . ak, (1)