2015/02/18 by Stuart Hannah, Hannah, Stuart A.
Computer Science · Mathematics · #05A15 #Advanced Combinatorial Mathematics #Bayesian Methods and Mixture Models #Census and Population Estimation #Combinatorics (math.CO) #FOS: Mathematics
paper · pdf · doi:10.48550/arxiv.1502.05340
openalex publication_date 2015/02/18 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Following a result of Eriksen and Sjöstrand (2014) we detail a technique to construct structures following the Fishburn distribution from appropriate Mahonian structures. This technique is introduced on a bivincular pattern of Bousquet-Mélou et al. (2010) and then used to introduce a previously unconsidered class of matchings; explicitly, zero alignment matchings according to the number of arcs which are both right-crossed and left nesting. We then define a statistic on the factorial posets of Claesson and Linusson (2011) counting the number of features which we refer to as mislabelings and demonstrate that according to the number of mislabelings that factorial posets follow the Fishburn distribution. As a consequence of our approach we find an identity for the Fishburn numbers in terms of the Mahonian numbers.