Details
| Original language | English |
|---|---|
| Pages (from-to) | 979-987 |
| Number of pages | 9 |
| Journal | Journal of algebraic combinatorics |
| Volume | 55 |
| Issue number | 3 |
| Early online date | 23 Oct 2021 |
| Publication status | Published - May 2022 |
Abstract
Let g1H1, … , gnHn be cosets of subgroups H1, … , Hn of a finite group G such that g1H1∪ … ∪ gnHn≠ G. We prove that | g1H1∪ … ∪ gnHn| ≤ γn| G| where γn< 1 is a constant depending only on n. In special cases, we show that γn= (2 n- 1) / 2 n is the best possible constant with this property and we conjecture that this is generally true.
Keywords
- Conjecture, Subgroup covering, Union of cosets
ASJC Scopus subject areas
- Mathematics(all)
- Algebra and Number Theory
- Mathematics(all)
- Discrete Mathematics and Combinatorics
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In: Journal of algebraic combinatorics, Vol. 55, No. 3, 05.2022, p. 979-987.
Research output: Contribution to journal › Article › Research › peer review
}
TY - JOUR
T1 - On the size of coset unions
AU - Sambale, Benjamin
AU - Tǎrnǎuceanu, Marius
N1 - Funding Information: We thank an anonymous reviewer for his/her valuable comments. The first author is supported by the German Research Foundation (SA 2864/1-2 and SA 2864/3-1).
PY - 2022/5
Y1 - 2022/5
N2 - Let g1H1, … , gnHn be cosets of subgroups H1, … , Hn of a finite group G such that g1H1∪ … ∪ gnHn≠ G. We prove that | g1H1∪ … ∪ gnHn| ≤ γn| G| where γn< 1 is a constant depending only on n. In special cases, we show that γn= (2 n- 1) / 2 n is the best possible constant with this property and we conjecture that this is generally true.
AB - Let g1H1, … , gnHn be cosets of subgroups H1, … , Hn of a finite group G such that g1H1∪ … ∪ gnHn≠ G. We prove that | g1H1∪ … ∪ gnHn| ≤ γn| G| where γn< 1 is a constant depending only on n. In special cases, we show that γn= (2 n- 1) / 2 n is the best possible constant with this property and we conjecture that this is generally true.
KW - Conjecture
KW - Subgroup covering
KW - Union of cosets
UR - http://www.scopus.com/inward/record.url?scp=85117681952&partnerID=8YFLogxK
U2 - 10.1007/s10801-021-01079-x
DO - 10.1007/s10801-021-01079-x
M3 - Article
AN - SCOPUS:85117681952
VL - 55
SP - 979
EP - 987
JO - Journal of algebraic combinatorics
JF - Journal of algebraic combinatorics
SN - 0925-9899
IS - 3
ER -