离散和超离散Toda分子初值问题解的组合表达式
Combinatorial expressions of the solutions to initial value problems of the discrete and ultradiscrete Toda molecules
摘要：
给出了离散和超离散Toda分子初值问题解的组合表达式。对于离散户田分子，减法自由表达的解决方案是来自非相交的路径，其中两个结果在组合学，Flajolet的解释连续分数和Gessel-Viennot的引理的决定因素，适用。通过超离散化无减法表达式，得到了超离散Toda分子的解。最后证明了超离散Toda分子的初值问题可以用特定图上的最短路来精确求解。
英文摘要：
Combinatorial expressions are presented to the solutions to initial value problems of the discrete and ultradiscrete Toda molecules. For the discrete Toda molecule, a subtraction-free expression of the solution is derived in terms of non-intersecting paths, for which two results in combinatorics, Flajolet's interpretation of continued fractions and Gessel--Viennot's lemma on determinants, are applied. By ultradiscretizing the subtraction-free expression, the solution to the ultradiscrete Toda molecule is obtained. It is finally shown that the initial value problem of the ultradiscrete Toda molecule is exactly solved in terms of shortest paths on a specific graph.
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