Description
CACAAG Seminar
Speaker: Neeraj Kumar.
Time: 5pm, Tuesday, 16 October 2018.
Venue: Ramanujan Hall.
Title: Wilf's conjecture on numerical semigroups
Abstract: The aim of the talk is to give a brief survey on the Wilf's
conjecture, and to present a commutative algebra formulation of it. We
will verify Wilf's conjecture in some cases.
A numerical semigroup $S$ is a subset of the nonnegative integers $N$ that
is closed under addition, contains 0, and has finite complement in $N$.
The Frobenius number $F$ of numerical semigroup $S$ is the largest integer
not in $S$. Let $d$ be the minimal number of generators of $S$ and $n$ be
the number of representable integers in the interval $[0, F]$. Wilf's
conjecture states that $F +1 \leq n d$.