Sieved Enumeration of Interval Orders and Other Fishburn Structures

Stuart A. Hannah

Published 2015-02-18Version 1

Following a result of Eriksen and Sj\"{o}strand 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-M\'elou 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) which we refer to as mislabelings and demonstrate that according to mislabelings 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.