One-Variable Word Equations and Three-Variable Constant-Free Word Equations
Saarela A; Nowotka D
One-Variable Word Equations and Three-Variable Constant-Free Word Equations
Saarela A
Nowotka D
WORLD SCIENTIFIC PUBL CO PTE LTD
Julkaisun pysyvä osoite on:
https://urn.fi/URN:NBN:fi-fe2021042719693
https://urn.fi/URN:NBN:fi-fe2021042719693
Tiivistelmä
We prove connections between one-variable word equations and three-variable constant-free word equations, and use them to prove that the number of equations in an independent system of three-variable constant-free equations is at most logarithmic with respect to the length of the shortest equation in the system. We also study two well-known conjectures. The first conjecture claims that there is a constant c such that every one-variable equation has either infinitely many solutions or at most c. The second conjecture claims that there is a constant c such that every independent system of three-variable constant-free equations with a nonperiodic solution is of size at most c. We prove that the first conjecture implies the second one, possibly for a different constant.
Kokoelmat
- Rinnakkaistallenteet [19206]