PreprintarXiv licencearXiv
The biwheel conjecture for braces
Abstract
Let b(n) denote the minimum number of perfect matchings in a simple brace of order n. De~Carvalho, Lucchesi and Murty (SIAM Journal on Discrete Mathematics, 27(2): (2013) 940-958) proved that b(n)≥(n−2)2/8 and conjectured that b(n)=(n−2)2/4 for all sufficiently large even n. We prove this conjecture.
Related
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- Determinant characters and multiplicative solubility of finite skew braces
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- Classification of finite left-simple skew braces
BibTeX
@misc{feng2026biwheel,
title = {{The biwheel conjecture for braces}},
author = {Xing Feng and Jinqiu Zhou},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.12955},
eprint = {2610.12955},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.12955},
}
RIS
TY - UNPB
TI - The biwheel conjecture for braces
AU - Xing Feng
AU - Jinqiu Zhou
PY - 2026
DA - 2026/10/09
PB - arXiv
DO - 10.48550/arxiv.2610.12955
UR - https://arxiv.org/abs/2610.12955
AB - Let b(n) denote the minimum number of perfect matchings in a simple brace of order n. De~Carvalho, Lucchesi and Murty (SIAM Journal on Discrete Mathematics, 27(2): (2013) 940-958) proved that b(n)≥(n−2)^2/8 and conjectured that b(n)=(n−2)^2/4 for all sufficiently large even n. We prove this conjecture.
ER -