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<blockquote data-quote="STay" data-source="post: 2100878" data-attributes="member: 225948">combinatorics, and elementary graph theory? I am a freshman in undergraduate college and was just accepted to an REU program. The specific project I was accepted to (which is the one I wanted) is a bit intimidating. I really have only had calculus and after this semester I&#039;ll have statistics and a course called random structures too (probability and randomness in discrete mathematics). So I&#039;m a bit underprepared for the program; here are the details:For this project we will consider rooted ordered trees avoiding other trees. In 2008, Rowland defined pattern avoidance in binary trees (i.e. trees where each vertex has either 0 or 2 children). The standard combinatorial sequences appear when enumerating such trees, and there exist bijections between these trees and other common combinatorial objects. There is also a method to determine equivalence classes of binary trees based on the number of trees that avoid them. This team will extend these known results about pattern avoidance to ternary trees (i.e. trees in which each vertex has 0 or 3 children).Prerequisites: linear algebra, or another proof based course; a course in combinatorics, discrete math, or elementary graph theory would be helpful.If anyone can recommend any books for self study for someone of my experience level (pretty easy to read) for simple introductions and elementary background info for these specific subjects? [combinatorics, linear algebra, set theory, graph theory, or anything that relates to this project]</blockquote>

[QUOTE="STay, post: 2100878, member: 225948"] combinatorics, and elementary graph theory? I am a freshman in undergraduate college and was just accepted to an REU program. The specific project I was accepted to (which is the one I wanted) is a bit intimidating. I really have only had calculus and after this semester I'll have statistics and a course called random structures too (probability and randomness in discrete mathematics). So I'm a bit underprepared for the program; here are the details: For this project we will consider rooted ordered trees avoiding other trees. In 2008, Rowland defined pattern avoidance in binary trees (i.e. trees where each vertex has either 0 or 2 children). The standard combinatorial sequences appear when enumerating such trees, and there exist bijections between these trees and other common combinatorial objects. There is also a method to determine equivalence classes of binary trees based on the number of trees that avoid them. This team will extend these known results about pattern avoidance to ternary trees (i.e. trees in which each vertex has 0 or 3 children). Prerequisites: linear algebra, or another proof based course; a course in combinatorics, discrete math, or elementary graph theory would be helpful. If anyone can recommend any books for self study for someone of my experience level (pretty easy to read) for simple introductions and elementary background info for these specific subjects? [combinatorics, linear algebra, set theory, graph theory, or anything that relates to this project] [/QUOTE]

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