Frobenius methods in combinatorics
Alessandro De Stefani, Jonathan Monta\~no, and Luis, N\'u\~nez-Betancourt
TL;DR
This paper surveys how Frobenius methods from prime characteristic algebra have advanced combinatorial commutative algebra, highlighting key results for ideals, varieties, and rings.
Contribution
It provides a comprehensive overview of Frobenius techniques applied to combinatorial algebra, including new insights into $F$-pure rings and monomial ideals.
Findings
Results for edge ideals, toric varieties, and Stanley-Reisner rings proven via Frobenius
Frobenius-like maps yield new results for monomial ideals
Insights into $F$-pure rings inspired by Stanley-Reisner ring work
Abstract
We survey results produced from the interaction between methods in prime characteristic and combinatorial commutative algebra. We showcase results for edge ideals, toric varieties, Stanley-Reisner rings, and initial ideals that were proven via Frobenius. We also discuss results for monomial ideals obtained using Frobenius-like maps. Finally, we present results for -pure rings that were inspired by work done for Stanley-Reisner rings.
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Taxonomy
TopicsCommutative Algebra and Its Applications · Algebraic structures and combinatorial models · Polynomial and algebraic computation