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| Auteurs principaux: | , |
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| Format: | Preprint |
| Publié: |
2026
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| Accès en ligne: | https://arxiv.org/abs/2605.22241 |
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| _version_ | 1866914587536785408 |
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| author | Banderier, Cyril Drmota, Michael |
| author_facet | Banderier, Cyril Drmota, Michael |
| contents | We provide a complete combinatorial and asymptotic analysis of positive linear systems of equations in one catalytic variable that appear in several combinatorial problems such as in lattice path counting or stack-sortable permutation counting.
We show that the corresponding generating functions satisfy a positive polynomial system of equations (which is associated to a context-free grammar). Furthermore we prove a universal asymptotic behaviour. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2605_22241 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Combinatorics and Asymptotics of Positive Systems of Linear Catalytic Equations Banderier, Cyril Drmota, Michael Combinatorics 05A15, 05A16 We provide a complete combinatorial and asymptotic analysis of positive linear systems of equations in one catalytic variable that appear in several combinatorial problems such as in lattice path counting or stack-sortable permutation counting. We show that the corresponding generating functions satisfy a positive polynomial system of equations (which is associated to a context-free grammar). Furthermore we prove a universal asymptotic behaviour. |
| title | Combinatorics and Asymptotics of Positive Systems of Linear Catalytic Equations |
| topic | Combinatorics 05A15, 05A16 |
| url | https://arxiv.org/abs/2605.22241 |