On the Möbius function and topology of general pattern posets

Smith, JP ORCID: https://orcid.org/0000-0002-4209-1604, 2019. On the Möbius function and topology of general pattern posets. Electronic Journal of Combinatorics, 26 (1): 1.49. ISSN 1077-8926

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Abstract

We introduce a formal definition of a pattern poset which encompasses several previously studied posets in the literature. Using this definition we present some general results on the Möbius function and topology of such pattern posets. We prove our results using a poset fibration based on the embeddings of the poset, where embeddings are representations of occurrences. We show that the Möbius function of these posets is intrinsically linked to the number of embeddings, and in particular to so called normal embeddings. We present results on when topological properties such as Cohen-Macaulayness and shellability are preserved by this fibration. Furthermore, we apply these results to some pattern posets and derive alternative proofs of existing results, such as Björner's results on subword order.

Item Type:	Journal article
Publication Title:	Electronic Journal of Combinatorics
Creators:	Smith, J.P.
Publisher:	Electronic Journal of Combinatorics
Date:	22 March 2019
Volume:	26
Number:	1
ISSN:	1077-8926
Identifiers:	Number Type 10.37236/7919 DOI 1390791 Other
Divisions:	Schools > School of Science and Technology
Record created by:	Linda Sullivan
Date Added:	21 Apr 2021 07:39
Last Modified:	17 Jan 2022 13:09
URI:	https://irep.ntu.ac.uk/id/eprint/42725

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