In this paper we study maximal chains in certain lattices constructed from powers of chains by iterated lax colimits in the 2-category of posets. Such a study is motivated by the fact that in lower dimensions, we get some familiar combinatorial objects such as Dyck paths and Kreweras walks.
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The authors would like to thank Sarah Selkirk for taking an interest in an early version of this paper and insightful discussions that followed, as well as some useful suggestions on the presentation.
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Janelidze, Z., Prodinger, H. & van Niekerk, F. Combinatorics Arising from Lax Colimits of Posets. Order (2023). https://doi.org/10.1007/s11083-022-09617-3
- Catalan number
- Distributive lattice
- Dyck path
- Fixed point
- Hermite history
- Kreweras walk
- Lax colimit
- Maximal chain number
- Noetherian form