Abstract
We introduce the poset of mesh patterns, which generalizes the permutation pattern poset. We fully classify the mesh patterns for which the interval [10̸,m] is non-pure, where 10̸ is the unshaded singleton mesh pattern. We present some results on the Möbius function of the poset, and show that μ(10̸,m) is almost always zero. Finally, we introduce a class of disconnected and non-shellable intervals by generalizing the direct product operation from permutations to mesh patterns.
Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
