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Algebra (Numata) Lab
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The lab studies enumerative combinatorics, using Young diagrams as a guide.
AboutAbout the lab
Structure emerges from counting
Prof. Numata studies combinatorial objects that appear in representation theory and ring theory from the viewpoint of enumerative combinatorics.
The main objects of study are Young diagrams, which control symmetric functions and irreducible representations.
The lab is interested in objects in general that admit combinatorial arguments, and also looks at structures that appear in computational algebraic statistics and topological data analysis.
For graduate studies, Prof. Numata is affiliated with the Graduate School of Information Science and Technology rather than the Graduate School of Science.
Key terms
- Enumerative combinatorics
- A field that studies how many arrangements or figures satisfy given conditions, starting from methods of counting
- Young diagram
- A diagram of boxes arranged in rows. A basic tool underlying calculations in symmetric functions and representation theory
- Representation theory
- A field that represents elements of algebra in concrete forms such as matrices and studies their structure
ResearchResearch themes
The lab investigates combinatorial objects that appear in representation theory and ring theory from the viewpoint of enumeration. With Young diagrams at the core, its interests extend broadly to any objects that admit combinatorial arguments.
*Illustrative imageYoung Diagrams and Symmetric Functions
The lab investigates combinatorial objects that appear in representation theory and ring theory from the viewpoint of enumerative combinatorics. Its main objects of study are Young diagrams, which control symmetric functions and irreducible representations.
*Illustrative imageCombinatorial Structures in Data Analysis
Recently, the lab has also become interested in the combinatorial structures that appear in the field known as computational algebraic statistics and in the method known as topological data analysis.
MembersFaculty
- ProfessorYasuhide Numata
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Report an errorAbout the images
The top and research theme images are illustrative and were not taken at the lab. They are cropped from Wikimedia Commons images. Cropped CC BY-SA images are provided under the same CC BY-SA license as the original (version shown on each line).
- Top image: “Young tableau for partitions of number 10” Unmismoobjetivo / CC BY 4.0 (cropped)
- Young Diagrams and Symmetric Functions: “Young 7642” ManiacParisien / CC BY-SA 3.0 (cropped)
- Combinatorial Structures in Data Analysis: “Blender3D VoronoiBasisCol2” SoylentGreen / CC BY-SA 3.0 (cropped)
- Related lab (Geometry Lab (Inoguchi)): “Hopf Fibration” Niles Johnson / CC BY 4.0 (cropped)
- Related lab (Kasuya Lab): “Standard contact structure r 3” Pmassot / CC BY-SA 3.0 (cropped)
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- Related lab (Hora Lab): “BMonSphere” Thomas Steiner / CC BY-SA 2.5 (cropped)
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