$λ$-fold near-factorizations of groups
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866915253622669312 |
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| author | Kreher, Donald L. Li, Shuxing Stinson, Douglas R. |
| author_facet | Kreher, Donald L. Li, Shuxing Stinson, Douglas R. |
| contents | We initiate the study of $λ$-fold near-factorizations of groups with $λ> 1$. While $λ$-fold near-factorizations of groups with $λ= 1$ have been studied in numerous papers, this is the first detailed treatment for $λ> 1$. We establish fundamental properties of $λ$-fold near-factorizations and introduce the notion of equivalence. We prove various necessary conditions of $λ$-fold near-factorizations, including upper bounds on $λ$. We present three constructions of infinite families of $λ$-fold near-factorizations, highlighting the characterization of two subfamilies of $λ$-fold near-factorizations. We discuss a computational approach to $λ$-fold near-factorizations and tabulate computational results for abelian groups of small order. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2503_09325 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | $λ$-fold near-factorizations of groups Kreher, Donald L. Li, Shuxing Stinson, Douglas R. Group Theory Combinatorics 05B10 We initiate the study of $λ$-fold near-factorizations of groups with $λ> 1$. While $λ$-fold near-factorizations of groups with $λ= 1$ have been studied in numerous papers, this is the first detailed treatment for $λ> 1$. We establish fundamental properties of $λ$-fold near-factorizations and introduce the notion of equivalence. We prove various necessary conditions of $λ$-fold near-factorizations, including upper bounds on $λ$. We present three constructions of infinite families of $λ$-fold near-factorizations, highlighting the characterization of two subfamilies of $λ$-fold near-factorizations. We discuss a computational approach to $λ$-fold near-factorizations and tabulate computational results for abelian groups of small order. |
| title | $λ$-fold near-factorizations of groups |
| topic | Group Theory Combinatorics 05B10 |
| url | https://arxiv.org/abs/2503.09325 |