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| Format: | Preprint |
| Publié: |
2026
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| Accès en ligne: | https://arxiv.org/abs/2603.22546 |
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| _version_ | 1866911559336329216 |
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| author | Lyudogovskiy, Fedor B. |
| author_facet | Lyudogovskiy, Fedor B. |
| contents | We study the partition graph $G_n$, whose vertices are the partitions of $n$ and whose edges correspond to elementary unit transfers between parts. We define the self-conjugate axis, its distance neighborhoods, and the thin spine, a first off-axis layer built from common neighbors of distinct axial vertices. We prove that distinct self-conjugate vertices are never adjacent, that the thin spine is a conjugation-invariant induced subgraph, and that axial and spinal concentration radii differ by at most one. Computations for $1 \le n \le 30$ show that the main local invariants are maximized near the axis and the spine. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2603_22546 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Axial Morphology of the Partition Graph: Self-Conjugate Axis, Spine, and Concentration Lyudogovskiy, Fedor B. General Mathematics 05A17, 05C75, 05C69, 05C12 We study the partition graph $G_n$, whose vertices are the partitions of $n$ and whose edges correspond to elementary unit transfers between parts. We define the self-conjugate axis, its distance neighborhoods, and the thin spine, a first off-axis layer built from common neighbors of distinct axial vertices. We prove that distinct self-conjugate vertices are never adjacent, that the thin spine is a conjugation-invariant induced subgraph, and that axial and spinal concentration radii differ by at most one. Computations for $1 \le n \le 30$ show that the main local invariants are maximized near the axis and the spine. |
| title | Axial Morphology of the Partition Graph: Self-Conjugate Axis, Spine, and Concentration |
| topic | General Mathematics 05A17, 05C75, 05C69, 05C12 |
| url | https://arxiv.org/abs/2603.22546 |