The Möbius function of permutations with an indecomposable lower bound

Brignall, Robert and Marchant, David William (2018). The Möbius function of permutations with an indecomposable lower bound. Discrete Mathematics, 341(5) pp. 1380–1391.

DOI: https://doi.org/10.1016/j.disc.2018.02.012

Abstract

We show that the Möbius function of an interval in a permutation poset where the lower bound is sum (resp. skew) indecomposable depends solely on the sum (resp. skew) indecomposable permutations contained in the upper bound, and that this can simplify the calculation of the Möbius sum. For increasing oscillations, we give a recursion for the Möbius sum which only involves evaluating simple inequalities.

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About

• Item ORO ID
• 53957
• Item Type
• Journal Item
• ISSN
• 0012-365X
• Academic Unit or School
• Faculty of Science, Technology, Engineering and Mathematics (STEM) > Mathematics and Statistics
  Faculty of Science, Technology, Engineering and Mathematics (STEM)
• Copyright Holders
• © 2018 Elsevier
• Related URLs
• • https://arxiv.org/abs/1710.03122(Other)
• Depositing User
• Robert Brignall