A 2D string is simply a 2D array. We continue the study of the combinatorial properties of repetitions in such strings over the binary alphabet, namely the number of distinct tandems, distinct quartics, and runs. First, we construct an infinite family of n× n 2D strings with Ω(n3) distinct tandems. Second, we construct an infinite family of n× n 2D strings with Ω(n2log n) distinct quartics. Third, we construct an infinite family of n× n 2D strings with Ω(n2log n) runs. This resolves an open question of Charalampopoulos, Radoszewski, Rytter, Waleń, and Zuba [ESA 2020], who asked if the number of distinct quartics and runs in an n× n 2D string is O(n2).
|Title of host publication||String Processing and Information Retrieval - 28th International Symposium, SPIRE 2021, Proceedings|
|Editors||Thierry Lecroq, Hélène Touzet|
|Publisher||Springer Science and Business Media Deutschland GmbH|
|Number of pages||14|
|State||Published - 2021|
|Event||28th International Symposium on String Processing and Information Retrieval, SPIRE 2021 - Virtual, Online|
Duration: 4 Oct 2021 → 6 Oct 2021
|Name||Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)|
|Conference||28th International Symposium on String Processing and Information Retrieval, SPIRE 2021|
|Period||4/10/21 → 6/10/21|
Bibliographical noteFunding Information:
P. Gawrychowski—Partially supported by the Bekker programme of the Polish National Agency for Academic Exchange (PPN/BEK/2020/1/00444). S. Ghazawi and G. M. Landau—Partially supported by the Israel Science Foundation grant 1475/18, and Grant No. 2018141 from the United States-Israel Binational Science Foundation (BSF).
© 2021, Springer Nature Switzerland AG.
- 2D strings
ASJC Scopus subject areas
- Theoretical Computer Science
- Computer Science (all)