OrientedSwaps

OrientedSwaps: a Mathematica package. The Mathematica package OrientedSwaps is a companion package to the 2019 paper ”Staircase Young tableaux, sorting networks and last passage percolation”: We present new combinatorial and probabilistic identities relating three random processes: the oriented swap process on n particles, the corner growth process, and the last passage percolation model. We prove one of the probabilistic identities, relating a random vector of last passage percolation times to its dual, using the duality between the Robinson-Schensted-Knuth and Burge correspondences. A second probabilistic identity, relating those two vectors to a vector of “last swap times” in the oriented swap process, is conjectural. We give a computer-assisted proof of this identity for n≤6 after first reformulating it as a purely combinatorial identity, and discuss its relation to the Edelman-Greene correspondence