Geometric constructions for Steinitz-type bounds in dimension two
Fuente:
arXiv
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| Autore principale: | |
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| Natura: | Preprint |
| Pubblicazione: |
2026
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| _version_ | 1866918393895976960 |
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| author | Pain, Jean-Christophe |
| author_facet | Pain, Jean-Christophe |
| contents | We investigate inequalities for partial sums of complex numbers with bounded modulus and zero total sum, a topic referred to as "polygonal confinement". Starting from Steinitz's classical result, we provide detailed constructions yielding explicit bounds, including $\sqrt{5}$, $\sqrt{3}$, $2$, and $\sqrt{2}$, depending on geometric constraints or weighted settings. The proofs are fully detailed with step-by-step constructions of permutations, highlighting the combinatorial and geometric intuition. We conclude with conjectures on optimal universal constants and directions for future research. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2603_16547 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Geometric constructions for Steinitz-type bounds in dimension two Pain, Jean-Christophe Combinatorics We investigate inequalities for partial sums of complex numbers with bounded modulus and zero total sum, a topic referred to as "polygonal confinement". Starting from Steinitz's classical result, we provide detailed constructions yielding explicit bounds, including $\sqrt{5}$, $\sqrt{3}$, $2$, and $\sqrt{2}$, depending on geometric constraints or weighted settings. The proofs are fully detailed with step-by-step constructions of permutations, highlighting the combinatorial and geometric intuition. We conclude with conjectures on optimal universal constants and directions for future research. |
| title | Geometric constructions for Steinitz-type bounds in dimension two |
| topic | Combinatorics |
| url | https://arxiv.org/abs/2603.16547 |