"Bouquet Algebra of

Toric Ideals"






(University of Bucharest)



Abstract: To any toric ideal (encoded by an integer matrix A) we associate a matroid structure called the bouquet graph of A, and introduce another toric ideal called the bouquet ideal of A, which captures the essential combinatorics of the initial toric ideal.  The new bouquet framework allows us to answer some open questions about toric ideals. For example, we provide  a characterization of toric ideals forwhich the following sets are equal: the Graver basis, the universal Groebner  basis,any reduced Groebner basis and any minimal generating set. Moreover, we show that toric ideals of hypergraphs encode all toric ideals.



Date:  Monday, March 30,  2015

Time: 10.40-11.30

Place: Mathematics Seminar Room, SA-141



All are most cordially invited.
Tea and biscuits: before the seminar