Tree generation and enumeration is an engaging and interesting but demanding book on tree generation and graph theory by Jesse Sakari Hyttinen. Released 28th Dec 2021 by the author, it's 150 pages and is available in paperback format.

This is an interesting concept: formalization of a system by which tree generation and enumeration can be more easily codified for study. The author has used a significant amount of effort to explain his methods for generating and classifying tree structures. Full of mathematical language which will likely be beyond the reach of most laypersons without either expert help, or a specialist background in allied subjects.

I am neither an expert in advanced algebra nor graph theory, although I have a significant background in biophysics, chemistry, and physics, and the necessary calculus and complex analysis to support those studies. I struggled to understand what the author was *trying* to say in this book. I didn't come away from the read with any clear understanding of how his method might differ from currently extant algorithms for tree generation (ramped half-and-half, PTC1, PTC2, randombranch, and uniform for example) except that his method is manual and the abovementioned are partially or wholly computer generated.

I also found the actual grammar tough going. It's not clear if the book was translated from Finnish or typeset/edited in English, but there are several places in the text which forced me to stop and interpret what the author was trying to say (grammatically, not mathematically).

There are no step by step proofs, although there are examples of generations of different sizes and complexity throughout the book.

Overall impression. I lack the specific expertise to make a valid judgement on the worth of the thesis to forward the study of graph theory or algebra. It's a deeply niche book and without the necessary background, I can't judge its suitability or correctness for classroom use in those disciplines. It's considerably beyond the scope of linear algebra and might be of use to graduate level graph theory studies.

The author is quite enthusiastic and the book is very well typeset. The eARC provided for review did not have an index, and it's unclear from the publishing info if there is an index in the final release copy.

Three stars with the *strong* codicil that my expertise in advanced mathematics might not have been up to the job. There are more accessible methods of tree generation and analysis currently available in my opinion.

Disclosure: I received an ARC at no cost from the author/publisher for review purposes.