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Abstract We continue our study of exponent semigroups of rational matrices. Our main result is that the matricial dimension of a numerical semigroup is at most its multiplicity (the least generator), greatly improving upon the previous upper bound (the conductor). For many numerical semigroups, including all symmetric numerical semigroups, our upper bound is tight. Our construction uses combinatorially structured matrices and is parametrised by Kunz coordinates, which are central to enumerative problems in the study of numerical semigroups.
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This content will become publicly available on February 28, 2026
Polygonal symplectic billiards
In this article, we study polygonal symplectic billiards. We provide new results, some of which are inspired by numerical investigations. In particular, we present several polygons for which all orbits are periodic. We demonstrate their properties and derive various conjectures using two numerical implementations.
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- Award ID(s):
- 2005444
- PAR ID:
- 10588148
- Publisher / Repository:
- AMR
- Date Published:
- Journal Name:
- Journal of the Association for Mathematical Research
- Volume:
- 1
- Issue:
- 1
- ISSN:
- 2998-4114
- Page Range / eLocation ID:
- 1 to 22
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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