Monday 6 May 2024 |
Events for day: Thursday 31 May 2018 |
9:30 - 10:30 Combinatorial Commutative Algebra Weekly Seminar Simon's Conjecture on Extendabily Shellable Simplicial Complexes and Chordality of Clutters School MATHEMATICS Let $I$ be a monomial ideal in the ring of polynomials $k[x_1,ldots,x_n]$ generated by $u_1,ldots, u_m$. It is called an ideal with linear quotients if the colon ideal $(u_1,ldots,u_i):(u_{i+1})$ is generated by linear forms, for each $1leq i< m$. A natural question is: For a given Ideal with linear quotients, is it possible to add a new monomial such that the new ideal again has linear quotients? The Simon's conjecture is an affirmative answer to this question in case that of all monomials have the same degree. In this talk, we show that this conjecture is related to the notion of simplicial elements in clutters and chordality of a compl ... |