Near-factorizations in association schemes

Abstract

We formally initiate the study of λ-fold (s,t) near-factorizations in association schemes. Namely, given an association (X, 𝒜), we consider the existence of a factorization of λ(J−I) into 01-matrices S and T with the constraint that S and T must belong to the adjacency algebra of (X, 𝒜). We establish basic properties of λ-fold (s,t) near-factorizations in association schemes and calculate bounds for λ, s, and t relative to the order of the association scheme. We completely determine all near-factorizations in symmetric and asymmetric 2-class association schemes. Furthermore, we construct near-factorizations in certain Hamming schemes, cyclotomic association schemes, Schurian schemes on small primitive groups, and the folded cube and halved cube association schemes. Finally, we establish that certain Hamming schemes, Johnson schemes, and Grassmann schemes do not admit a λ-fold near-factorization.

Dual near-factorizations and Schur products in association schemes
Bobby Miraftab, Sho Suda
arXiv25 Oct 2026PreprintCC BY 4.0Full textCombinatorics & discrete mathematicsarXiv
High-order uniformly accurate fully discrete schemes with long time near-conservations for two nonlinear coupled dispersive models in the nonrelativistic regime
Lina Wang, Jiyong Li, Bin Wang
arXiv12 Oct 2026PreprintarXiv licenceFull textNumerical analysis & scientific computingarXiv
DNN-Assisted Near-Optimal Codebook Design for Uplink SCMA Schemes over Rician Fading Channels
Wasif Ali, Yen-Ming Chen, Fan-Shuo Tseng
arXiv28 Sep 2026PreprintarXiv licenceFull textGeneral mathematicsarXiv
On separability of Tatra association schemes
Grigory Ryabov
arXiv25 Oct 2026PreprintarXiv licenceFull textCombinatorics & discrete mathematicsarXiv
Schrijver-Delsarte rigidity in association schemes and undecidability of quantum graph homomorphism
Lorenzo Ciardo, Iris Hebbeker, Gideo Joubert +2
arXiv17 Sep 2026PreprintCC BY 4.0Full textAnalysis & PDEs Combinatorics & discrete mathematicsarXiv

Cite

BibTeX RIS

BibTeX

@misc{herman2026nearfactorizations,
  title = {{Near-factorizations in association schemes}},
  author = {Allen Herman and Alice Lacaze-Masmonteil and Karen Meagher and Hermie Monterde},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2610.07394},
  eprint = {2610.07394},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2610.07394},
}

RIS

TY  - UNPB
TI  - Near-factorizations in association schemes
AU  - Allen Herman
AU  - Alice Lacaze-Masmonteil
AU  - Karen Meagher
AU  - Hermie Monterde
PY  - 2026
DA  - 2026/10/05
PB  - arXiv
DO  - 10.48550/arxiv.2610.07394
UR  - https://arxiv.org/abs/2610.07394
AB  - We formally initiate the study of λ-fold (s,t) near-factorizations in association schemes. Namely, given an association (X, 𝒜), we consider the existence of a factorization of λ(J−I) into 01-matrices S and T with the constraint that S and T must belong to the adjacency algebra of (X, 𝒜). We establish basic properties of λ-fold (s,t) near-factorizations in association schemes and calculate bounds for λ, s, and t relative to the order of the association scheme. We completely determine all near-factorizations in symmetric and asymmetric 2-class association schemes. Furthermore, we construct near-factorizations in certain Hamming schemes, cyclotomic association schemes, Schurian schemes on small primitive groups, and the folded cube and halved cube association schemes. Finally, we establish that certain Hamming schemes, Johnson schemes, and Grassmann schemes do not admit a λ-fold near-factorization.
ER  -

Abstract

Related

Cite