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Expositio paper exp-20261020-281c1b

Kepler Towers (Catalan Objects)

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In this paper, we will dive into the deep world of Catalan numbers, exploring interesting examples and why those are Catalan objects. There will be a special focus on Kepler Towers, one specific type of Catalan object that seems to be relatively unstudied a…

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exp-20261020-281c1bv1 Latest public version Public since October 20, 2026 Submitted October 20, 2026 0 saves
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Mathematics / Combinatorics
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Other designs, configurations
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exp-20261020-281c1bv1
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Authors

Justin Cheong (Mountain View High School)

Abstract

In this paper, we will dive into the deep world of Catalan numbers, exploring interesting examples and why those are Catalan objects. There will be a special focus on Kepler Towers, one specific type of Catalan object that seems to be relatively unstudied and has a nonobvious bijection with Dyck words, another Catalan object.

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Mathematics
Main field
Combinatorics Designs and configurations Other designs, configurations
Mathematics
Main field
Combinatorics Enumerative combinatorics Combinatorial identities, bijective combinatorics
Mathematics
Main field
Combinatorics Enumerative combinatorics Exact enumeration problems, generating functions

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exp-20261020-281c1bv1

Kepler Towers (Catalan Objects)

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Uploaded Oct 20, 2026 335103 bytes Selected Latest
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