| Project/Area Number |
24740059
|
|---|
| Research Category |
Grant-in-Aid for Young Scientists (B)
|
| Allocation Type | Multi-year Fund |
|---|
| Research Field |
General mathematics (including Probability theory/Statistical mathematics)
|
|---|
| Research Institution | Kyoto University |
|---|
Principal Investigator |
|
|---|
| Project Period (FY) |
2012-04-01 – 2014-03-31
|
| Project Status |
Completed (Fiscal Year 2013)
|
| Budget Amount *help |
¥1,560,000 (Direct Cost: ¥1,200,000、Indirect Cost: ¥360,000)
Fiscal Year 2013: ¥780,000 (Direct Cost: ¥600,000、Indirect Cost: ¥180,000)
Fiscal Year 2012: ¥780,000 (Direct Cost: ¥600,000、Indirect Cost: ¥180,000)
|
|---|
| Keywords | 数理物理 / 可積分系 / 組合せ論 / 行列式 / Aztec diamond / 非交叉径路 / タイリング / 完全マッチング / 非交叉格子路 |
|---|
| Research Abstract |
The Hankel transform makes a new sequence of numbers from a given sequence of numbers by computing Hankel determinants of the given numbers. In this study the Hankel transform is examined from the viewpoint of discrete integrable systems having determinant solutions which relate with combinatorial objects such as lattice paths. The results are applied to initial value problems of discrete integrable systems. Especially combinatorial expressions in terms of non-intersecting lattice paths are given to the exact solutions to the initial value problems of the discrete Toda molecules and related integrable systems. Furthermore a tiling problem of the Aztec diamond is also investigated. To the Aztec diamond theorem a new proof is exhibited by using discrete integrable systems with the help of orthogonal functions.
|
