黃大原（Tayuan Huang）教授

聯絡方式

• Email: thuang@math.nctu.edu.tw
• 電話: 03-571-2121 ext. 56417
• 傳真: 03-572-4679
• 地址: 新竹市大學路1001號 交通大學 應用數學系
• 相關網站:    

近兩學期教授課程

• 111 學年度第一學期：
  • 離散數學


• 111 學年度第二學期：
  • 基礎圖論

履歷

• 學歷
  • 私立中原大學 數學系 學 士 (1972)
  • 國立清華大學數學研究所碩士(1976)
  • 俄亥俄州立大學 數學系 博 士 (1985
• 學術專長暨研究領域
  • 代數組合學
  • 有限幾何
  • 組合設計
• 學術經歷與榮譽

  私立中原大學電子工程學系講師 1976/08 － 1978/07 私立輔仁大學 電子工程學系 講 師 1978/08 － 1979/07 國立交通大學 應用數學系所 副 教 授 1985/08 － 1989/07 國立交通大學 應用數學系所 教 授 1989/08 － 國科會數學推動中心委員（1992 －1995) 國科會自然處學學學門審議委員 1997/02 － 1998/08 國科會優良研究獎 (1989) 教育部教學優良獎 (1993)



• 近五年研究計劃
  • 關於幾類正則圖形值譜性值之研究(1/3)(97-2115-M-009-004-)
  • 關於強正則多重圖及其相關有限幾何的研究(3/3)(96-2115-M-009-002-)
  • 關於強正則多重圖及其相關有限幾何的研究(2/3)(95-2115-M-009-007-)
  • 關於強正則多重圖及其相關有限幾何的研究(1/3)(94-2115-M-009-015-)
  • 關於組合設計理論及其相關應用的研究(3/3)(93-2115-M-009-003- )
  • 關於組合設計理論及其相關應用的研究(2/3)(92-2115-M-009-006- )
  • 關於組合設計理論及其相關應用的研究(1/3)(91-2115-M-009-012- )

研究趣向

P-多項式結合方案(P-polynomial association schemes)是一類源於統計實驗設計，且具有高度正則性、對稱性的組合結構，與其它數學分支如群論、直交多項式、lattices、度量空間、編碼、組合設計等的關連，日益密切。這類組合結構也以距離正則圖形 (distance regular graphs) 的形式活躍於代數組合學的範疇裡。過去多年的研究工作，就是針對伴隨距離正則圖形的高度正則性和對稱性而來的；

1. 有限幾何結構---幾何上的制約
2. 相交參數 (intersection array)---組合的制約
3. 值譜 (spectral)---線性代數的制約
4. Bose-Mesner代數---代數的制約 來進行

為建立三度空間裡紐結 (knots) 的多項式不變量，Jones 和Kauffman等人於1984-1989前後引進對稱旋量模式(symmetric spin models)的觀念，並進而推廣到二重、四重旋量模式 (two-weight, four-weight spin models)。我們在四重旋量模式和Bose-Mesner algebras之間建立明確關係，提供階段性的結論以及後續研究的基礎。

我們目前的主要研究興趣，在於探討結合方案、距離正則圖形在pooling designs所扮演的角色。

著作選集

(A)   Refereed Papers：

1. Tayuan Huang (with T. S. Fu), “A characterization of two classes of strongly regular graphs”, Journal of Geometry, 52(1995), 91-100.
2. Tayuan Huang (with P. Guan), “A note on the coloring of a certain class of graphs”, The Journal of Combinatorial mathematics and Combinatorial Computing, 18(1995), 125-127.
3. Tayuan Huang (with T. S. Fu), “Quasi-semisymmetric designs with extremal conditions”, Journal of Statistical Planning and Inferences, 51(1996), 261-271., 計畫編號：NSC81-0208-M009-33
4. Tayuan Huang (with M. Deza), “Complementary L1-graphs and related combinatorial structures:, Lecture Notes in Computer Science 1120, Springer-Verlag, pp.74-90(1996), 計畫編號：NSC82-0208-M009-014 (simultaneous as LIENS 94-12, Ecole Normale Superieuri, Paris)
5. Tayuan Huang (with M. Deza), “L1-embeddability of some block graphs and cycloids”, Bulletin of the Institute of Mathematics, Academia Sinica, 24(1996), 87-102., 計畫編號：NSC83-0208-M009-26 (simultaneous as LIENS 94-13, Ecole Normale Superieuri, Paris)
6. Tayuan Huang (with M. Deza), “Metrics on Permutations, a Survey”, Journal of Combinatorics, Information and System Sciences, Vol. 23, Nos. 1-4, 173-185(1998)., 計畫編號：NSC85-2121-M009-012 (simultaneous as LIENS-97-1, Ecole Normale Superieuri, Paris)
7. Tayuan Huang (with C. R. Liu), “Spectral Characterization of Generalized Odd Graphs”, Graphs and Combinatorics, 15(1999) 195-209.
8. Tayuan Huang (with Y. Chang), “Imprimitive Symmetric Association Schemes of Low Ranks and Higmanian Graphs”, Annals of Combinatorics, 4(2000) 317-326.
9. Tayuan Huang (with H. Guo), “Some classes of four-weight spin models”, Journal of Statistical Planning and Inference, 4(2000) 410-412.
10. Tayuan Huang (with H. Guo), “Some Remarks on Four-weight Spin Models”, Annals of Combinatorics, 94(2001) 231-247.
11. Tayuan Huang (with Michel Deza), “A Generalization of Strongly Regular Graphs”, South-East Asian Bulletin of Math. Society, (2002)26, 193-201.
12. Tayuan Huang (with Chih-Wen Weng) A Note on Decoding of Superimposed Codes, Journal of Combinatorial Optimization 7, 381-384, 2003.
13. Huang (with K.H. You) “Strongly Regular Graphs associated with Bent Functions”, The Proceedings of the 7th Symposium on Parallel Architectures, Algorithms and Networks, IEEE 380-383, 2004.
14. Tayuan Huang (with Chih-Wen Weng) Pooling Spaces and Non-Adaptive Pooling Designs, Discrete Mathematics 282 (2004) 163-169.
15. Tayuan Huang* (with Kaishun Wang, Chih-wen Wang) Pooling Spaces associated with Finite geometry, European Journal of Combinatorics 29(2008) 1483-1491.
16. Tayuan Huang* (Lingling Huang, and Miaow-Ing Lin) On a Class of Strongly Regular Designs and Quasi-semisymmetric Designs, Recent Developments of Algebra and Related Areas, Advanced Lecture in Mathematics 8, pp.129-153, Higher Education Press and International Press, Beijing and Boston, 2009.
17. Tayuan Huang* (with Kaishun Wang and Chih-wen Weng) A Class of Error-Correcting Pooling Designs on Complexes, Journal of Combinatorial Optimization, to appear.
18. Tayuan* (with Guang-Siang Lee) An extension of the Stein-Lovasz Theorem and some of its applications, preprint 2008.

(B)   Conference Papers：

1. Tayuan Huang (1995), “The Erdos-Ko-Rado Type Result on Quantum Matroids”, Hyperhraphs and Symmetric Structures: A Combinatorial Conference of the Bolyai Society, Balatonelle Hungary, June 19-23.
2. Tayuan Huang (1996), “Four-weight spin models and related Bose-Mesner Algebras”, 1996 Shanghai Conference on Designs, codes and Finite Geometries, Shanghai, May 15-19, 1996; The 13th Symposium on Algebraic Combinatorics, Sapporo Japan, July 1-3, 1996.
3. Tayuan Huang (1997), “On quasi-semisymmetric designs”, Finite Geometry and Combinatorics, Third International Conference at Deinze, Belgium, May 18-24, 1997, (partially supported by NSC).
4. Tayuan Huang (1997), “Some Combinatorial Structures Supported by Bose-Mesner algebras”, The 5-th Franco-Taiwanese International Conference on Combinatorics and Computer Science, September 15-18, (partially supported by NSC).
5. Tayuan Huang (1998), “Some remarks on Four-weight spin models”, Combinatorics and Physics ’98, Los Alamos, New Mexico USA, August 10-12, (partially supported by NSC).
6. Tayuan Huang (1999), “Distance-Regularity and Spectra of Graphs”, Third Shanghai Conference on Designs, Codes and Finite Geometries, May 14-18, Shanghai Jiao-Tung University (partially supported by NCTU).
7. Tayuan Huang (1999), “Geometric Characterization of Some Distance-Regular Graphs”, International Conference on Graph Theory and Combinatorics, Changwon National University and Com2 Mathematics Center POSTECH, August 10-19 (partially supported by KOSEF, Korea).
8. Tayuan Huang (2000), “A Technique for Spectral Characterization of Some Graphs”, Workshops on Algebra and Combinatorics, March 27-30, The Chinese University Hong Kong.
9. Tayuan Huang (2002), “On dual pairs of set system”, Satellite Conference on Combinatorics. ICM 2002, Shijiazhuang, August 16-19, 2002.
10. Tayuan Huang (2003) “Strongly Regular Designs”, The Second East Asian Conference on Algebra and Combinatorics EACAC2, Kyushu University Fukuoka Japan, November 17-21, 2003.
11. Tayuan Huang (2004) “Strongly Regular Graphs associated with Bent Functions”, Symposium on Parallel Architectures, Algorithms and Networks, The University of Hong Kong, May 10-12, 2004.12
12. Tayuan Huang (2004) “ Error-Correcting Pooling Designs and Their Decoding”, International Conference in Disccrete Mathematics with Applications to Information Science and Related Topics, Chongqing, October 18-25, 2004.

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