论文标题
在几个变量中用于分析组合学的同型技术
Homotopy techniques for analytic combinatorics in several variables
论文作者
论文摘要
我们将来自同型持续求解器的工具与几个变量中的分析组合方法相结合，以提供第一个实用算法和实现多元理性生成函数的渐近学，而不是依靠非依赖于非符合性的``合并'''非合并性的'非静态性假设。我们的同质实施在三个变量中终止了文献中的示例，我们还描述了启发式方法，这些方法终止并正确预测在更高维度中的示例中在合理时间内正确预测渐近行为。我们的结果是通过使用homotopyContinature.jl软件包在Julia中实现的，我们提供了一些示例和基准。
We combine tools from homotopy continuation solvers with the methods of analytic combinatorics in several variables to give the first practical algorithm and implementation for the asymptotics of multivariate rational generating functions not relying on a non-algorithmically checkable `combinatorial' non-negativity assumption. Our homotopy implementation terminates on examples from the literature in three variables, and we additionally describe heuristic methods that terminate and correctly predict asymptotic behaviour in reasonable time on examples in even higher dimension. Our results are implemented in Julia, through the use of the HomotopyContinuation.jl package, and we provide a selection of examples and benchmarks.
