Counting quadrant walks via Tutte's invariant method
Overview
Paper Summary
This paper adapts Tutte's invariant method to analyze quadrant walks, proving algebraicity for several models, including Gessel's. It introduces a weaker invariant notion, demonstrating D-algebraicity for nine non-D-finite models with decoupling functions, using a novel integral-free expression for their generating function.
Explain Like I'm Five
Scientists figured out a clever way to count different paths you can draw on a special grid, moving only up or right. They found secret rules that show how many paths there are, making it easier to predict them.
Possible Conflicts of Interest
Supported by NSF and the European Research Council - no obvious conflicts identified.
Identified Limitations
Rating Explanation
A strong paper extending Tutte's invariant method to quadrant walks, providing new algebraic and D-algebraic results. The heavy use of computer algebra in some proofs and the limited scope slightly lower the rating.
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