2025/10/08 by M. Ram Murty, Murty, M. Ram, Naik, Sunil
Mathematics · #05B35 #06A07 #06C10 #11A25 #11N35 #11N37 #Combinatorics (math.CO) #FOS: Mathematics #History and Theory of Mathematics #Mathematics and Applications #Number Theory (math.NT) #Point processes and geometric inequalities
paper · pdf · doi:10.48550/arxiv.2510.07046
openalex publication_date 2025/10/08 · openalex created_date 2025/10/18 · openalex updated_date 2026/07/28
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.