Morneau-Guérin, Frédéric 
ORCID: https://orcid.org/0000-0001-7610-4648 et Singh, Sarishti
(07 aout 2026).
The arithmetic complexity of Erdős matrices. Communication (sur invitation) présentée à International Workshop on Operator Theory and its Applications (IWOTA) 2026, Québec.
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- iwota2026_final_beamer.pdf
Contenu du fichier : Diaporama Accès restreint jusqu'à fin- 1 janvier 2027. |
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| Catégorie de document : | Communications à des congrès/colloques et conférences (non publiées) |
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| Évaluation par un comité de lecture : | Non |
| Étape de publication : | Non publié |
| Résumé : | Erdős matrices are the doubly stochastic matrices for which equality holds in the Marcus–Ree inequality max_{sigma in S_n}\sum_{i=1}^n a_{i, sigma(i)} >= \|A\|_F^2 where the left-hand side denotes the largest diagonal sum of the matrix and the right-hand side denotes the Frobenius norm of the matrix. Recent work has shown that every Erdős matrix has rational entries and is uniquely determined by the positions of its zero entries. This naturally raises a quantitative arithmetic question: how complicated can these rational entries become? A natural measure of this complexity is the size of the least common denominator of the matrix entries. In this talk, we initiate the study of this arithmetic complexity by investigating the growth of the largest denominator that can occur in a given dimension. We present the first general lower and upper bounds, obtained through a combination of block constructions, graph-theoretic methods, and a representation-theoretic approach. |
| Adresse de la version officielle : | https://iwota-2026.fsg.ulaval.ca/ |
| Déposant: | Morneau-Guérin, Frédéric |
| Responsable : | Frédéric Morneau-Guérin |
| Dépôt : | 11 aout 2026 17:32 |
| Dernière modification : | 16 aout 2026 13:48 |
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