Restricted lego towers

Toufik Mansour, Matthias Schork, Armend Sh Shabani

Research output: Contribution to journalArticlepeer-review


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.

Original languageEnglish
Pages (from-to)61-76
Number of pages16
JournalJournal of Automata, Languages and Combinatorics
Issue number1
StatePublished - 2020

Bibliographical note

Publisher Copyright:
©Institut für Informatik · Justus-Liebig-Universität Giessen.


  • Area
  • Generating functions
  • Lego towers
  • Perimeter

ASJC Scopus subject areas

  • Discrete Mathematics and Combinatorics
  • Computational Theory and Mathematics


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