Discrete Math Seminar: Bridget Tenner

We will discuss a sorting phenomenon for data in a rectangular array, called the "non-messing-up" property. Consider a collection of distinct numbers arranged in a rectangle. The non-messing-up property says that if you put the numbers of each row into increasing order, and then do the same thing to the (possibly new) numbers of each column, then the (possibly new) numbers in each row will still be in increasing order. In other words, the "in increasing order" feature of the rows doesn't get messed up, even though the values in the rows may change! We will explore what it means to generalize this property, and will look at some of these generalizations in detail.