Simplicial complexes associated to certain subsets of natural numbers and its applications to multiplicative functions
| dc.creator | Snellman, Jan | |
| dc.date | 2002-11-13 | |
| dc.date.accessioned | 2026-07-07T04:52:53Z | |
| dc.date.available | 2026-07-07T04:52:53Z | |
| dc.description | We call a set of positive integers closed under taking unitary divisors a unitary ideal. It can be regarded as a simplicial complex. Moreover, a multiplicative arithmetical function on such a set corresponds to a function on the simplicial complex with the property that the value on a face is the product of the values at the vertices of that face. We use this observation to solve the following problems: 1) Let r be a positive integer and c a real number. What is the maximum value that \sum_{s \in S}g(s) can obtain when S is a unitary ideal containing precisely r prime powers, and g is the multiplicative function determined by g(s)=c when s \in S is a prime power? 2) Suppose that g is a multiplicative function which is \ge 1, and that we want to find the maximum of g(i) when 1 \le i \le n. At how many integers do we need to evaluate g? | |
| dc.description | 9 pages, LaTeX2e Keywords: Multiplicative arithmetical functions, simplicial complexes, linear extensions, boolean termorders | |
| dc.identifier | https://arxiv.org/abs/math/0211201 | |
| dc.identifier | http://arxiv.org/abs/math/0211201 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/65635 | |
| dc.subject | Combinatorics | |
| dc.subject | Number Theory | |
| dc.subject | 05E25; 11A25 | |
| dc.title | Simplicial complexes associated to certain subsets of natural numbers and its applications to multiplicative functions | |
| dc.type | text |