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arXiv:1810.10428math.CO

Enumeration of $S$-omino towers and row-convex $k$-omino towers

Alexander M. Haupt

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Abstract

We first enumerate a generalization of domino towers that was proposed by Tricia M. Brown (J. Integer Seq. 20 (2017)), which we call S-omino towers. We establish equations that the generating function must satisfy and then apply the Lagrange inversion formula to find a closed formula for the number of towers. We also show a connection to generalized Dyck paths and provide an explicit bijection. Finally, we consider the set of row-convex k-omino towers, introduced by Brown, and calculate an exact generating function.

arXiv comments
This new version additionally includes an explicit bijective proof for S-omino towers
Journal reference
DOI
Subjects
math.COCombinatorics

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  1. Is this Duplo train track under too much tension? 1 comment

    • Look into the work of Søren Eilers https://arxiv.org/abs/math/0504039 https://www.tandfonline.com/doi/abs/10.4169/amer.math.monthl... (for the latter: use sci-hub) Then there is also work for the 2D case by Tricia Muldoon Brown…

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