Fantastic Patterns and Where Not to Find Them

Interesting patterns are everywhere we look, but what happens when we try to avoid patterns? A permutation is a list of numbers in a specific order. When we avoid a pattern, we try not to order those numbers in certain ways. For example, the permutation 45312 avoids the 123 pattern because no three elements in the permutation are in an increasing order. In our work, we studied the permutations that avoid two different patterns of length three. We focused on the distribution of peaks, valleys, double ascents, and double descents over these sets of permutations