Characterization of Erdös matrices by their zero entries
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arXiv
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| Hauptverfasser: | , , , |
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| Format: | Preprint |
| Veröffentlicht: |
2025
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| _version_ | 1866917353105653760 |
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| author | Karmakar, Priyanka Krishna, Hariram Pal, Souvik Teja, G. Krishna |
| author_facet | Karmakar, Priyanka Krishna, Hariram Pal, Souvik Teja, G. Krishna |
| contents | An Erdös matrix $E$ is a bistochastic matrix whose sum of squares of entries (Frobenius norm squared) equals its maxtrace (maximum of all the $σ$-traces for permutations $σ$'s). We characterize all Erdös $E$ by the patterns of their zero entries; showing that each such skeleton has at most one $E$. We present an algorithm to find all $n\times n$ Erdös matrices, which finds them up to $n\leqslant 5$ quickly and also size $n=6$. We further show some presently known RCDS matrices to be Erdös. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2512_04766 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Characterization of Erdös matrices by their zero entries Karmakar, Priyanka Krishna, Hariram Pal, Souvik Teja, G. Krishna Combinatorics Metric Geometry 15A15 (primary), 15A45, 15B36, 15B51 (secondary) An Erdös matrix $E$ is a bistochastic matrix whose sum of squares of entries (Frobenius norm squared) equals its maxtrace (maximum of all the $σ$-traces for permutations $σ$'s). We characterize all Erdös $E$ by the patterns of their zero entries; showing that each such skeleton has at most one $E$. We present an algorithm to find all $n\times n$ Erdös matrices, which finds them up to $n\leqslant 5$ quickly and also size $n=6$. We further show some presently known RCDS matrices to be Erdös. |
| title | Characterization of Erdös matrices by their zero entries |
| topic | Combinatorics Metric Geometry 15A15 (primary), 15A45, 15B36, 15B51 (secondary) |
| url | https://arxiv.org/abs/2512.04766 |