The Eulerian numbers can D.I.E
Fuente:
arXiv
Saved in:
| Main Authors: | , |
|---|---|
| Format: | Preprint |
| Published: |
2025
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866917100958777344 |
|---|---|
| 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 |