Counting square free monomial cremona maps
B\'arbara Costa, Thiago Dias, Rodrigo Gondim, Ricardo Machado

TL;DR
This paper classifies all square-free Cremona maps with up to six variables and develops an algorithm to enumerate such transformations, extending the classification to seven variables.
Contribution
It provides a complete classification for up to six variables and introduces an algorithm to count monomial square-free Cremona transformations, extending to seven variables.
Findings
Complete list of square-free Cremona maps with ≤6 variables.
Algorithm for counting monomial square-free Cremona transformations.
Extended classification to 7 variables.
Abstract
We give a complete list of square-free Cremona maps with at most six variables, up to equivalence classes. We also build an algorithm to count monomial square-free Cremona transformations. Using this algorithm, we obtain a complete list of monomial square-free Cremona transformations in seven variables.
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Taxonomy
TopicsAdvanced Combinatorial Mathematics · Advanced Topics in Algebra · Homotopy and Cohomology in Algebraic Topology
