Complex sentence: Gilbreath permutations can be characterized by the property that every prefix contains a consecutive set of numbers; in terms of permutation patterns, they are the permutations that avoid the two patterns 132 and 312.
Split into simpler sentences: Gilbreath permutations can be characterized by the property that every prefix contains a consecutive set of numbers. Equivalently, in terms of permutation patterns, the Gilbreath permutations are the permutations that avoid the two patterns 132 and 312.