Counting Self-Dual Interval Orders

Abstract

In this paper, we present a new method to derive formulas for the generating functions of interval orders, counted with respect to their size, magnitude, and number of minimal and maximal elements. Our method allows us not only to generalize previous results on refined enumeration of general interval orders, but also to enumerate self-dual interval orders with respect to analogous statistics. Using the newly derived generating function formulas, we are able to prove a bijective relationship between self-dual interval orders and upper-triangular matrices with no zero rows. Previously, a similar bijective relationship has been established between general interval orders and upper-triangular matrices with no zero rows and columns.

20 pages

References in corpus (4)

• (2+2)-free posets, ascent sequences and pattern avoiding permutations
• Enumerating (2+2)-free posets by indistinguishable elements
• Wilf classification of bi-vincular permutation patterns
• Two New Interpretations of the Fishburn Numbers and their Refined Generating Functions

Cited by in corpus (6)

• Enumeration of Irredundant Forests
• On q-Series Identities Related to Interval Orders
• Sieved Enumeration of Interval Orders and Other Fishburn Structures
• A new decomposition of ascent sequences and Euler--Stirling statistics
• Congruences for Taylor expansions of quantum modular forms
• Self-dual interval orders and row-Fishburn matrices