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In a recent paper by Kitaev and Remmel, several formulas for the number ofwords of length n avoiding some generalized patterns were established. Eachtime the obtained function of n had been found in Sloane's Encyclopedia as thenumber of some other objects, but the bijections between the two sets did notfollow from the proof. Kitaev and Remmel stated four open problems on findingrespective bijections. Here we solve two of them, concerning sequences A007070and A048739.

Two bijections for sets of words with forbidden factors