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Counting shared sites of three friendly directed lattice paths and related problems

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Counting shared sites of three friendly directed lattice paths and related problems
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23
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CC Attribution - NonCommercial - NoDerivatives 4.0 International:
You are free to use, copy, distribute and transmit the work or content in unchanged form for any legal and non-commercial purpose as long as the work is attributed to the author in the manner specified by the author or licensor.
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We study the enumeration of three friendly directed walks on the square lattice. We show how one can count different types of shared sites (interactions) by solving the associated functional equations using the obstinate kernel method. However, we also highlight that the introduction of finer counting problems that introduce asymmetry can lead to as yet unsolvable functional equations. We survey related results over the past few years counting extra features in multiple path problems.
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