Two particular families of polyominoes are introduced and enumerated, namely so-called k-Lego towers and cone k-Lego towers. The first family consists of Lego towers containing in each floor exactly one piece having length less than or equal to k. The generating function for the number of k-Lego towers as well as cone k-Lego towers with n floors according to a statistic given by perimeter and area is determined. Furthermore, for the number of cone k-Lego towers with exactly n floors an explicit formula is derived. In addition, several special cases are treated in detail.
|Number of pages||16|
|Journal||Journal of Automata, Languages and Combinatorics|
|State||Published - 2020|
Bibliographical notePublisher Copyright:
©Institut für Informatik · Justus-Liebig-Universität Giessen.
- Generating functions
- Lego towers
ASJC Scopus subject areas
- Discrete Mathematics and Combinatorics
- Computational Theory and Mathematics