| Title: |
Harmonious sequences in groups with a unique involution |
| Authors: |
de Wolf, Lydia; Javaheri, Mohammad |
| Source: |
Combinatorial Theory, vol 5, iss 3 |
| Publisher Information: |
eScholarship, University of California |
| Publication Year: |
2025 |
| Collection: |
University of California: eScholarship |
| Subject Terms: |
Sequenceable groups; Latin squares; harmonious groups; complete mappings |
| Description: |
We study several combinatorial properties of finite groups that are related to the notions of sequenceability, R-sequenceability, and harmonious sequences. In particular, we show that in every abelian group \(G\) with a unique involution \(\imath_G\) there exists a permutation \(g_0,\ldots, g_{m}\) of elements of \(G \backslash \{\imath_G\}\) such that the consecutive sums \({g_0+g_1, g_1+g_2,\ldots, g_{m}+g_0}\) also form a permutation of elements of \(G\backslash \{\imath_G\}\). We also show that in every abelian group of order at least 4 there exists a sequence containing each non-identity element of \(G\) exactly twice such that the consecutive sums also contain each non-identity element of \(G\) twice. We apply several results to the existence of transversals in Latin squares.Mathematics Subject Classifications: 05E16, 20D60, 05B15Keywords: Sequenceable groups, Latin squares, harmonious groups, complete mappings |
| Document Type: |
article in journal/newspaper |
| File Description: |
application/pdf |
| Language: |
unknown |
| Relation: |
qt5489614t; https://escholarship.org/uc/item/5489614t; https://escholarship.org/content/qt5489614t/qt5489614t.pdf |
| DOI: |
10.5070/C65365556 |
| Availability: |
https://escholarship.org/uc/item/5489614t; https://escholarship.org/content/qt5489614t/qt5489614t.pdf; https://doi.org/10.5070/C65365556 |
| Rights: |
CC-BY |
| Accession Number: |
edsbas.EB448B84 |
| Database: |
BASE |