Vol. 12, No. 9, 2018

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Random flag complexes and asymptotic syzygies

Daniel Erman and Jay Yang

Vol. 12 (2018), No. 9, 2151–2166
Abstract

We use the probabilistic method to construct examples of conjectured phenomena about asymptotic syzygies. In particular, we use Stanley–Reisner ideals of random flag complexes to construct new examples of Ein and Lazarsfeld’s nonvanishing for asymptotic syzygies and of Ein, Erman, and Lazarsfeld’s conjecture on how asymptotic Betti numbers behave like binomial coefficients.

Keywords
syzygies, monomial ideals
Mathematical Subject Classification 2010
Primary: 13D02
Secondary: 05C80, 13F55, 14J40
Milestones
Received: 21 September 2017
Revised: 21 May 2018
Accepted: 15 July 2018
Published: 21 December 2018
Authors
Daniel Erman
Department of Mathematics
University of Wisconsin
Madison, WI
United States
Jay Yang
Department of Mathematics
University of Minnesota Twin Cities
Minneapolis 55455