Unordered Rooted Ternary Trees: A Sage-Powered Combinatorial Adventure
This blog post tackles the challenging problem of counting unordered rooted ternary trees using analytic combinatorics, specifically the Flajolet-Sedgewick method. The author first solves the simpler case of ordered trees, deriving an asymptotic approximation via generating functions and singularity analysis, all implemented and verified in Sage. The more complex unordered case is then addressed using Pólya-Redfield counting, leading to a numerical solution and asymptotic formula, again validated with Sage. The post provides a clear and engaging explanation of complex analysis concepts such as Puiseux series and offers readily usable Sage code, making it a valuable resource for those interested in the intersection of algorithms and mathematics.