An elementary approach to solve recursions relative to the enumeration of S-Motzkin paths
Helmut Prodinger
TL;DR
This paper introduces elementary linear algebra techniques to solve recursions related to counting S-Motzkin paths, which are bijective to ternary trees, simplifying their enumeration process.
Contribution
It presents a novel elementary approach to solving recursions for S-Motzkin paths, avoiding complex methods.
Findings
Derived explicit formulas for S-Motzkin paths enumeration
Established elementary linear algebra methods for path counting
Simplified the recursive calculations for related combinatorial structures
Abstract
S-Motzkin paths (bijective to ternary trees) and partial version of them are calculated using only elementary methods from linear algebra.
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