Pure Mathematics Colloquium: An expression for the Möbius function µ[σ,π] of the permutation pattern poset based on intervals in π

Speaker: David Marchant (The Open University)

Title: An expression for the Möbius function µ[σ,π] of the permutation pattern poset based on intervals in π

Microsoft Teams Meeting

Abstract:

Balloon permutations are formed from the merge of two permutations, α and β, and have the property that β occurs as an interval copy in the balloon permutation. Any permutation can be expressed as a balloon permutation.

We find an expression for the Möbius function of balloon permutations in terms of a sum over a set of permutations, plus a correction factor.

We show that for certain types of balloon permutation (“wedge permutations'') the correction factor is always zero. Further, we show that the principal Möbius function of a wedge permutation is always a multiple of the principal Möbius function of β.