Billey, Jockusch, and Stanley characterized 321-avoiding permutations by a property of their reduced decompositions. This paper generalizes that result with a detailed study of permutations via their reduced decompositions and the notion of pattern containment. These techniques are used to prove a new characterization of vexillary permutations in terms of their principal dual order ideals in a ...

Motivated by the problem of constructing bijective maps with low differential uniformity, we introduce notion permutation resemblance a function, which looks to measure distance given map is from being permutation. We prove several results concerning permutation resemblance and show how it can ...