COMPUTING RATIONAL POWERS OF MONOMIAL IDEALS

Authors

• PRATIK DONGRE, Indian Institute of Information Technology
• BENJAMIN DRABKIN, Singapore University of technology and Design
• JOSIAH LIM, Johns Hopkins University
• ETHAN PARTIDA, Brown University
• ETHAN ROY, The University of Texas at Austin
• DYLAN RUFF, University of Toronto
• Alexandra Seceleanu, University of Nebraska-LincolnFollow
• TINGTING TANG, San Diego State University

Document Type

Article

Date of this Version

8-31-2022

Citation

Journal of Symbolic Computation, 116, pp. 39-57

Comments

Used by permission.

Abstract

This paper concerns fractional powers of monomial ideals. Rational powers of a monomial ideal generalize the integral closure operation as well as recover the family of symbolic powers. They also highlight many interesting connections to the theory of convex polytopes. We provide multiple algorithms for computing the rational powers of a monomial ideal. We also introduce a mild generalization allowing real powers of monomial ideals. An important result is that given any monomial ideal I, the function taking a real number to the corresponding real power of I is a step function which is left continuous and has rational discontinuity points.