| Budget Amount *help |
¥4,680,000 (Direct Cost: ¥3,600,000、Indirect Cost: ¥1,080,000)
Fiscal Year 2018: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000)
Fiscal Year 2017: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000)
Fiscal Year 2016: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000)
Fiscal Year 2015: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000)
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| Outline of Final Research Achievements |
In the joint work with A. Hoshino, we studied the explicit formula (for the transition matrices or brunching rules) for the Koornwinder polynomials associated with one column diagrams. It was shown that the matrix inversion formulas of Bressoud or Krattenthaler play the central role in these combinatorial objects, i.e. the transition matrices. As applications, we proved that the entries of the transition matrix from the monomial polynomials to the Macdonald polynomials of type C satisfy an analogue of the recurrence relations for the Catalan triangle numbers, and also proved that the Kostka polynomials are given by the q-Catalan numbers.
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