Brun's inequality for a geometric lattice
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_ | 1866908581916311552 |
|---|---|
| author | Murty, M. Ram Naik, Sunil |
| author_facet | Murty, M. Ram Naik, Sunil |
| contents | In a seminal paper of 1915, V. Brun introduced Brun's sieve, which is based on Brun's inequality for the Möbius function and is a very powerful tool in modern number theory. The importance of the Möbius function in enumeration problems led G.-C. Rota to introduce the concept of the Möbius function to partially ordered sets. In this article, we prove Brun's inequality for geometric lattices and develop a sieve in this context. One of the main ingredients is a recent work of K. Adiprasito, J. Huh, and E. Katz on the log-concavity of absolute values of the Whitney numbers associated with matroids. We also study shifted convolutions of the Whitney numbers associated with Dowling lattices. Further, we derive an asymptotic formula for generalized Dowling numbers. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2510_07046 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Brun's inequality for a geometric lattice Murty, M. Ram Naik, Sunil Number Theory Combinatorics 05B35, 06A07, 06C10, 11A25, 11N35, 11N37 In a seminal paper of 1915, V. Brun introduced Brun's sieve, which is based on Brun's inequality for the Möbius function and is a very powerful tool in modern number theory. The importance of the Möbius function in enumeration problems led G.-C. Rota to introduce the concept of the Möbius function to partially ordered sets. In this article, we prove Brun's inequality for geometric lattices and develop a sieve in this context. One of the main ingredients is a recent work of K. Adiprasito, J. Huh, and E. Katz on the log-concavity of absolute values of the Whitney numbers associated with matroids. We also study shifted convolutions of the Whitney numbers associated with Dowling lattices. Further, we derive an asymptotic formula for generalized Dowling numbers. |
| title | Brun's inequality for a geometric lattice |
| topic | Number Theory Combinatorics 05B35, 06A07, 06C10, 11A25, 11N35, 11N37 |
| url | https://arxiv.org/abs/2510.07046 |