2021/10/19 by Bouvel, Mathilde, Cioni, Lapo, Izart, Benjamin · 1 citation
#Combinatorics (math.CO) #FOS: Mathematics
paper · doi:10.48550/arxiv.2110.10000
The interval poset of a permutation is the set of intervals of a permutation, ordered with respect to inclusion. It has been introduced and studied recently in [B. Tenner, arXiv:2007.06142]. We study this poset from the perspective of the decomposition trees of permutations, describing a procedure to obtain the former from the latter. We then give alternative proofs of some of the results in [B. Tenner, arXiv:2007.06142], and we solve the open problems that it posed (and some other enumerative problems) using techniques from symbolic and analytic combinatorics. Finally, we compute the Möbius function on such posets.