| _version_ | 1866901222078808064 |
|---|---|
| author | JOVIČEVIĆ, SAŠA |
| author_facet | JOVIČEVIĆ, SAŠA |
| contents | <p> <strong>Contact: </strong><a rel="noopener">sasa.jov.ubl@gmail.com</a>.</p> <p>Among universal constructions valid for all degrees $k$, the classical solution of Prouhet based on the Thue--Morse sequence occupies a central position.. Its defining feature is an underlying orthogonality that enforces a highly regular and sparse internal structure. This raises a fundamental structural question that has received little explicit attention:</p> <blockquote> <p><em><strong>Why not consider universal non-orthogonal construction while preserving the cardinality $2^k$?</strong></em></p> </blockquote> <p>In this paper, we answer this question affirmatively by exhibiting an explicit non-orthogonal recursive construction.<br>The loss of orthogonality allows for substantially richer local configurations.<br>In particular, the resulting sets may contain desired longer consecutive integer runs than those permitted by the Thue--Morse construction, while still satisfying all moment identities up to degree $k$ and preserving the classical bound $2^k$.</p> <p> <strong>Cite as: </strong> Saša Jovičević (2026), <strong>Non-Orthogonal Universal Construction for the Prouhet–Tarry–Escott Problem</strong>, Zenodo.</p> |
| format | Recurso digital |
| id | zenodo_https___doi_org_10_5281_zenodo_18402664 |
| institution | Zenodo |
| language | |
| publishDate | 2026 |
| publisher | Zenodo |
| record_format | zenodo |
| spellingShingle | Non-Orthogonal Universal Construction for the Prouhet–Tarry–Escott Problem JOVIČEVIĆ, SAŠA Prouhet--Tarry--Escott problem equal sums of like powers non-orthogonal recursive construction first-difference symmetry consecutive integer runs <p> <strong>Contact: </strong><a rel="noopener">sasa.jov.ubl@gmail.com</a>.</p> <p>Among universal constructions valid for all degrees $k$, the classical solution of Prouhet based on the Thue--Morse sequence occupies a central position.. Its defining feature is an underlying orthogonality that enforces a highly regular and sparse internal structure. This raises a fundamental structural question that has received little explicit attention:</p> <blockquote> <p><em><strong>Why not consider universal non-orthogonal construction while preserving the cardinality $2^k$?</strong></em></p> </blockquote> <p>In this paper, we answer this question affirmatively by exhibiting an explicit non-orthogonal recursive construction.<br>The loss of orthogonality allows for substantially richer local configurations.<br>In particular, the resulting sets may contain desired longer consecutive integer runs than those permitted by the Thue--Morse construction, while still satisfying all moment identities up to degree $k$ and preserving the classical bound $2^k$.</p> <p> <strong>Cite as: </strong> Saša Jovičević (2026), <strong>Non-Orthogonal Universal Construction for the Prouhet–Tarry–Escott Problem</strong>, Zenodo.</p> |
| title | Non-Orthogonal Universal Construction for the Prouhet–Tarry–Escott Problem |
| topic | Prouhet--Tarry--Escott problem equal sums of like powers non-orthogonal recursive construction first-difference symmetry consecutive integer runs |
| url | https://doi.org/10.5281/zenodo.18402664 |