Let's say I'm writing a GA to find an optimal path to travel from point $A$ to point $B$. Genotypes are a list of directions (north, south, east, west) to follow.
So a genotype "NENWEE" will move north once, east once, then north again, west once, and finally east twice.
The directions are encoded as follows:
N : 00 E : 01 W : 10 S : 11
Our first genotype, "NENWEE" (let's call it $P$), will thus be encoded as follows: $00\,01\,00\,10\,01\,01$
Let $Q$ be a second genotype, say "EENEWW", which is encoded as follows: $01\,01\,00\,01\,10\,10$
Now let's do a one-point crossover operation on genotype $Q$, from $P$. The randomly-chosen crossover point is between the $9$-th and $10$-th bit, so bits $10$, $11$ and $12$ from genotype $P$ will replace those same bits from genotype $Q$. Let's call the resulting genotype $Q'$.
P : 00 01 00 10 01 01 Q : 01 01 00 01 10 10 Q' : 01 01 00 01 11 01
After decoding $Q'$ we find that the result is "EENESE". However neither $P$ nor $Q$ contained direction south.
My question is, do crossover operators imply a certain degree of mutation by definition?