A Mahonian d-function is a Mahonian statistic that can be expressed as a linear combination of vincular pattern functions of length at most d. Babson and Steingrímsson classified all Mahonian 3-functions up to trivial bijections and identified many of them with well-known Mahonian statistics in the literature. We prove a host of Mahonian 3-function equidistributions over permutations in S_n avoiding a single classical pattern in S_3. Tools used include block decomposition, Dyck paths and generating functions.
NATURVETENSKAP -- Matematik (hsv//swe)
NATURAL SCIENCES -- Mathematics (hsv//eng)
NATURVETENSKAP -- Matematik -- Diskret matematik (hsv//swe)