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| Autores principales: | , |
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| Formato: | Preprint |
| Publicado: |
2025
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| Materias: | |
| Acceso en línea: | https://arxiv.org/abs/2511.19076 |
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| _version_ | 1866917100958777344 |
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| author | Konvalinka, Matjaž Petersen, T. Kyle |
| author_facet | Konvalinka, Matjaž Petersen, T. Kyle |
| contents | The Eulerian numbers form a triangular array with many interesting properties. The numbers arise from various combinatorial and probabilistic interpretations, and have been studied in a variety of mathematical contexts. In this article we examine two distinct alternating sign formulas for the Eulerian numbers and show how they can be proved using a sign-reversing involution technique described by Benjamin and Quinn known as the ``D.I.E.'' method. Each of these arguments lends itself to a broad generalization, shedding light on different parts of mathematics. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2511_19076 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | The Eulerian numbers can D.I.E Konvalinka, Matjaž Petersen, T. Kyle Combinatorics The Eulerian numbers form a triangular array with many interesting properties. The numbers arise from various combinatorial and probabilistic interpretations, and have been studied in a variety of mathematical contexts. In this article we examine two distinct alternating sign formulas for the Eulerian numbers and show how they can be proved using a sign-reversing involution technique described by Benjamin and Quinn known as the ``D.I.E.'' method. Each of these arguments lends itself to a broad generalization, shedding light on different parts of mathematics. |
| title | The Eulerian numbers can D.I.E |
| topic | Combinatorics |
| url | https://arxiv.org/abs/2511.19076 |