The m-Cover Posets and their applications
- Autor(en)
- Myrto Kallipoliti, Henri Mühle
- Abstrakt
In this article we introduce the m-cover poset of an arbitrary bounded poset P, which is a certain subposet of the m-fold direct product of P with itself. Its ground set consists of multichains of P that contain at most three different elements, one of which has to be the least element of P, and the other two elements have to form a cover relation in P. We study the m-cover poset from a structural and topological point of view. In particular, we characterize the posets whose m-cover poset is a lattice for all m>0, and we characterize the special cases, where these lattices are EL-shellable, left-modular, or trim. Subsequently, we investigate the m-cover poset of the Tamari lattice
Tn, and we show that the smallest lattice that contains the m-cover poset of
Tn is isomorphic to the m-Tamari lattice Tn(m) introduced by Bergeron and Préville-Ratelle. We conclude this article with a conjectural desription of an explicit realization of Tn(m) in terms of m-tuples of Dyck paths.
- Organisation(en)
- Institut für Mathematik
- Externe Organisation(en)
- Université Paris VII - Paris-Diderot
- Journal
- Advances in Applied Mathematics
- Band
- 69
- Seiten
- 65-108
- Anzahl der Seiten
- 44
- ISSN
- 0196-8858
- DOI
- https://doi.org/10.1016/j.aam.2015.06.001
- Publikationsdatum
- 08-2015
- Peer-reviewed
- Ja
- ÖFOS 2012
- 101012 Kombinatorik
- Schlagwörter
- ASJC Scopus Sachgebiete
- Applied Mathematics
- Link zum Portal
- https://ucris.univie.ac.at/portal/de/publications/the-mcover-posets-and-their-applications(ca3eb0e7-e9e7-4a51-9763-aa31eff360d1).html