On a question of Eliahou and a conjecture of Wilf

• Type: Article in International Scientific Journal
• Date: 2018

Authors

delgado, m (Author) FCUP

Journal

Title: Mathematische Zeitschrift

Vol. 288

Pages: 595-627

ISSN: 0025-5874

Publisher: Springer Nature

Indexing

ISI Web of Knowledge - 13 Citations

Scopus - 15 Citations

Other information

Authenticus ID: P-00M-SR6

DOI: 10.1007/s00209-017-1902-3

Abstract (EN): To a numerical semigroup S, Eliahou associated a number and proved that numerical semigroups for which the associated number is non negative satisfy Wilf's conjecture. The search for counterexamples for the conjecture of Wilf is therefore reduced to semigroups which have an associated negative Eliahou number. Eliahou mentioned 5 numerical semigroups whose Eliahou number is . The examples were discovered by Fromentin who observed that these are the only ones with negative Eliahou number among the over numerical semigroups of genus up to 60. We prove here that for any integer n there are infinitely many numerical semigroups S such that , by explicitly giving families of such semigroups. We prove that all the semigroups in these families satisfy Wilf's conjecture, thus providing not previously known examples of semigroups for which the conjecture holds.

Language: English

Type (Professor's evaluation): Scientific

No. of pages: 33