| Budget Amount *help |
¥4,940,000 (Direct Cost: ¥3,800,000、Indirect Cost: ¥1,140,000)
Fiscal Year 2016: ¥1,300,000 (Direct Cost: ¥1,000,000、Indirect Cost: ¥300,000)
Fiscal Year 2015: ¥780,000 (Direct Cost: ¥600,000、Indirect Cost: ¥180,000)
Fiscal Year 2014: ¥780,000 (Direct Cost: ¥600,000、Indirect Cost: ¥180,000)
Fiscal Year 2013: ¥780,000 (Direct Cost: ¥600,000、Indirect Cost: ¥180,000)
Fiscal Year 2012: ¥1,300,000 (Direct Cost: ¥1,000,000、Indirect Cost: ¥300,000)
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| Outline of Final Research Achievements |
We studied toric rings of configurations constructed by a method with symmetries such as a centrally symmetric configuration, and discussed various algebraic properties of toric rings and ideals. In particular, we introduced the notion of “configurations of harmony” which yields more reflexive polytopes than the notion of centrally symmetric configurations. In addition, we studied toric ideals arising from various combinatorial objects. For example, we showed that the convex polytope arising from the centrally symmetric configuration of any order polytope is a normal reflexive polytope.
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