| Budget Amount *help |
¥2,600,000 (Direct Cost: ¥2,000,000、Indirect Cost: ¥600,000)
Fiscal Year 2012: ¥780,000 (Direct Cost: ¥600,000、Indirect Cost: ¥180,000)
Fiscal Year 2011: ¥780,000 (Direct Cost: ¥600,000、Indirect Cost: ¥180,000)
Fiscal Year 2010: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000)
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| Research Abstract |
We found and proved a new mathematical formula in the field of combinatorics. That is called a fermionic formula for partition functions associated with level set of a periodic integrable cellular automaton. By inventing a cellular-automaton-like description in terms of two colored strips, we also succeeded to construct a family of commuting phase flows (generalized time evolutions) in tropical periodic Toda lattice, a special discrete limit of well known Toda lattice in the field of classical integrable systems. The phase flows are important to determine the structure of the phase space of this dynamical system.
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