Enumerative combinatorics on matchings and its application

• Project/Area Number: 25800009
• Research Category: Grant-in-Aid for Young Scientists (B)
• Allocation Type: Multi-year Fund
• Research Field: Algebra
• Research Institution: Shinshu University
• Principal Investigator: NUMATA Yasuhide 信州大学, 学術研究院理学系, 准教授 (00455685)
• Project Period (FY): 2013-04-01 – 2017-03-31
• Project Status: Completed (Fiscal Year 2016)
• Budget Amount: ¥4,160,000 (Direct Cost: ¥3,200,000、Indirect Cost: ¥960,000); Fiscal Year 2016: ¥650,000 (Direct Cost: ¥500,000、Indirect Cost: ¥150,000); Fiscal Year 2015: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000); Fiscal Year 2014: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000); Fiscal Year 2013: ¥1,690,000 (Direct Cost: ¥1,300,000、Indirect Cost: ¥390,000)
• Keywords: 母関数 / 数え上げ / ヤング図形 / マッチング / 組合せ論 / 平面二分木 / 数え上げ組合せ論 / 代数的組合せ論 / 表現論的組合せ論 / Grothendieck polynomial / Cauchy formula / マッチング数 / 既約ピタゴラス数

Outline of Final Research Achievements

We studied on matchings ingraphs mainly, and obatained some results on enumerative combinatorics by this research.
We showed the uniqueness of the family of triples whose mathing numbers are pitagorian tripes in some condition. We also obtained some results on Young diagrams and Young tableaux.

Research Products

• [Journal Article] Toward a combinatorial formula for an irregular conformal block of rank one (2017)
  • Author(s): Nagoya, Hajime / Numata, Yasuhide
  • Journal Title: Josai Mathematical Monographs (Representation Theory and Differential Equations : Proceedings of JMM Workshop on Representation Theory and Differential Equations,November 26-27,2023 Josai University) Volume: 10 Pages: 81-95
  • NAID: 120006028483
  • Peer Reviewed / Acknowledgement Compliant
• [Journal Article] On graphs whose Hosoya indices are primitive Pythagorean triples (2016)
  • Author(s): Tomoe Kadoi, Yasuhide Numata
  • Journal Title: Notes on Number Theory and Discrete Mathematics Volume: 22 Pages: 59-80
  • Peer Reviewed / Open Access / Acknowledgement Compliant
• [Presentation] On combinatorics of a K-theoretic analogue of Schur functions. (2015)
  • Author(s): Yasuhide NUMATA
  • Organizer: Workshop and Seminar on Topological Combinatorics and Related Topics
  • Place of Presentation: Kasetsart University, Bangkok, Thailand
  • Year and Date: 2015-01-07
• [Presentation] On graphs whose Hosoya indices are primitive Pythagorean triples (2014)
  • Author(s): Tomoe KADOI, Yasuhide NUMATA
  • Organizer: Japan Conference on Graph Theory and Combinatorics
  • Place of Presentation: Nihon University
  • Year and Date: 2014-05-17
• [Book] The Lefschetz Properties, Lecture Notes in Mathematics, Vol. 2080 (2013)
  • Author(s): Harima, T.; Maeno, T.; Morita, H.; Numata, Y.; Wachi, A.; Watanabe, J.
  • Total Pages: 250
  • Publisher: Springer Berlin Heidelberg