On the Number of Compositions of Two Polycubes

Authors

  • Andrei Asinowski Alpen-Adria-Universität Klagenfurt
  • Gill Barequet Technion -- Israel Inst. of Technology
  • Gil Ben-Shachar Technion -- Israel Inst. of Technology
  • Martha Carolina Osegueda Univ. of California, Irvine
  • Günter Rote Freie Universität Berlin

DOI:

https://doi.org/10.57717/cgt.v3i1.41

Abstract

A composition of two polycubes is appending them to each other so that the union is a valid polycube. We provide almost tight (up to subpolynomial factors) bounds on the minimum and maximum possible numbers of compositions of two polycubes, either when each is of size n, or when their total size is N, in two and higher dimensions. We also provide an efficient algorithm for computing the number of compositions that two given polyominoes (or polycubes) have.

 

Downloads

Published

2024-06-18

How to Cite

Asinowski, A., Barequet, G., Ben-Shachar, G., Osegueda, M. C., & Rote, G. (2024). On the Number of Compositions of Two Polycubes. Computing in Geometry and Topology, 3(1), 4:1–4:18. https://doi.org/10.57717/cgt.v3i1.41

Issue

Vol. 3 No. 1 (2024)

Section

Original Research Articles

Categories

License

Copyright (c) 2024 Andrei Asinowski, Gill Barequet, Gil Ben-Shachar, Martha Carolina Osegueda, Günter Rote

Creative Commons License

This work is licensed under a Creative Commons Attribution 4.0 International License.

Authors who publish with this journal agree to the following terms:

Authors retain copyright and grant the journal right of first publication with the work simultaneously licensed under a Creative Commons Attribution License that allows others to share the work with an acknowledgement of the work's authorship and initial publication in this journal.

Authors are able to enter into separate, additional contractual arrangements for the non-exclusive distribution of the journal's published version of the work (e.g., post it to an institutional repository or publish it in a book), with an acknowledgement of its initial publication in this journal.

Authors are permitted and encouraged to post their work online (e.g., in institutional repositories or on their website) prior to and during the submission process, as it can lead to productive exchanges, as well as earlier and greater citation of published work (See The Effect of Open Access).