| Budget Amount *help |
¥4,420,000 (Direct Cost: ¥3,400,000、Indirect Cost: ¥1,020,000)
Fiscal Year 2018: ¥1,300,000 (Direct Cost: ¥1,000,000、Indirect Cost: ¥300,000)
Fiscal Year 2017: ¥1,690,000 (Direct Cost: ¥1,300,000、Indirect Cost: ¥390,000)
Fiscal Year 2016: ¥1,430,000 (Direct Cost: ¥1,100,000、Indirect Cost: ¥330,000)
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| Outline of Final Research Achievements |
A plane partition is a two-dimensional array of non-negative integers which weakly decrease along each row and column. In this study a method is formulated to find nice (product) formulas for (reverse) plane partitions from biorthogonal polynomials and from solutions to the discrete two-dimensional (2D) Toda lattice, that is a dynamical system associated with biorthogonal polynomials. New nice formulas which generalizes some of the existing generating functions for (reverse) plane partitions, such as MacMahon's generating function and the trace generating function, are derived from a specific family of biorthogonal polynomials and from a specific solution to the discrete 2D Toda lattice.
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