English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Plus annual

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Plus monthly

Global: Zendy Tools annual

Global: Zendy Tools monthly

Global: Zendy Free Plan

We present a two term formula for the M\"obius function of intervals in theposet of all permutations, ordered by pattern containment. The first term inthis formula is the number of so called normal occurrences of one permutationin another. Our definition of normal occurrences is similar to those that haveappeared in several variations in the literature on the M\"obius function ofthis and other posets, but simpler than most of them. The second term in theformula is complicated, but we conjecture that it equals zero for a significantproportion of intervals. We present some cases where the second term vanishesand others where it is nonzero. Computing the M\"obius function recursivelyfrom its definition has exponential complexity, whereas the computation of thefirst term in our formula is polynomial and the exponential part is isolated tothe second term, which seems to often vanish. We also present a result on theM\"obius function of posets connected by a poset fibration.

A Formula for the M\"obius function of the Permutation Poset Based on a Topological Decomposition