Make up a class of rooted trees with restrictions on the number of Children at each vertex. Use the decomposition of the tree into the root and the subtrees which are children of the root to get an equation which the generating series for this class satisfies. Check that your answer is likely to be correct by calculating the first few terms by counting by hand and check that this works in the equation you got (you can use a computer for this last part if you like). Now you can make as many examples as you like and check your answers.
Make up a class of rooted trees with restrictions on the number of Children at each vertex. Use the decomposition of the tree into the root and the subtrees which are children of the root to get an equation which the generating series for this class satisfies. Check that your answer is likely to be correct by calculating the first few terms by counting by hand and check that this works in the equation you got (you can use a computer for this last part if you like). Now you can make as many examples as you like and check your answers.
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Transcribed Image Text:Make up a class of rooted trees with restrictions on the number of
children at each vertex. Use the decomposition of the tree into the root and the
subtrees which are children of the root to get an equation which the generating series
for this class satisfies. Check that your answer is likely to be correct by calculating
the first few terms by counting by hand and check that this works in the equation
you got you can use a computer for this last part if you like). Now you can make as
many examples as you like and check your answers.
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