2020/04/03 by Fulman, Jason, Petersen, T. Kyle
#05A05 #60C05 #Combinatorics (math.CO) #FOS: Mathematics #Probability (math.PR)
paper · doi:10.48550/arxiv.2004.01659
In this expository article, we highlight the direct connection between card shuffling and the functions known as P-partitions that come from algebraic combinatorics. While many (but not all) of the results we discuss are known, we give a unified treatment. The key idea is this: the probability of obtaining a permutation π from shelf shuffling is the probability that a random P-partition is sorted by π, and the probability of obtaining π from riffle shuffling is the probability that a random P-partition is sorted by π-1.