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Tree generation and enumeration: A collection of mathematical ideas in graph theory

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Have you seen the movie Good Will Hunting? There was this problem in math that was quite easy, according to many, but seemed to lack a structured, formal proof. Even worse was the fact that there are infinitely many problems of the exact same kind and again, without any systematic way to prove them! That is where my TGET (Tree generation and enumeration) comes in...

I believe in inspiring and connecting people with mathematics. I also believe in sharing knowledge and passing it on to further generations. By making books and building a community for graph theory and treespeak enthusiasts, I can show people that mathematics is a form of art, a pinnacle of creativity, and a competitive game as well.

Whether you are a mathematician, student, teacher, enthusiast or hobbyist, I think this book can awaken your curiosity, and help you in your mathematical journeys. Especially if you would like to know about tree generation and enumeration, how trees are linked to partitions and what a Peano-like axiomatic system for rooted trees looks like.

Treespeak is about the subtle cooperation between vertex edge algebra and the tree generation algorithm.

150 pages, Paperback

Published December 1, 2021

About the author

A mathematician, programmer and author, passionate user of symbolic and partition form treespeak. Has a couple of programming projects as a hobby, such as Qiybz and Treespeak.

Has a lifelong goal of inspiring people and sharing knowledge with others, all with the power of mathematics in a book form. Interests include topics such as mathematics, science, music and video games.

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Profile Image for Annie.
4,710 reviews85 followers
March 25, 2022
Originally posted on my blog: Nonstop Reader.

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.
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