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Properties of Lyubeznik numbers under localization and polarization
Arindam Banerjee, Luis Núñez-Betancourt, Kohji Yanagawa
We exhibit a global bound for the Lyubeznik numbers of a ring of prime characteristic. In addition, we show that for a monomial ideal, the Lyubeznik numbers of the quotient rings o…
Regularity of Path Ideals of Gap Free Graphs
Arindam Banerjee
In this paper we study the Castelnuovo-Mumford regularity of the path ideals of finite simple graphs. We find new upper bounds for various path ideals of gap free graphs. In partic…
Powers of edge ideals of regularity three bipartite graphs
Ali Alilooee, Arindam Banerjee
In this paper we prove that if is a bipartite edge ideal with regularity three then for all the regularity of is exactly .
The Regularity of Powers of Edge Ideals
Arindam Banerjee
In this paper we prove the existence of a special order on the set of minimal monomial generators of powers of edge ideals of arbitrary graphs. Using this order we find new upper b…