Updated on 2024/06/06

写真a

 
TAGAWA Hiroyuki
 
Name of department
Faculty of Education, Mathematics Education
Job title
Professor
Concurrent post
Faculty of Education（Dean）
Mail Address
E-mail address
Homepage
External link

Education

  • The University of Tokyo   数理科学研究科   数理科学  

Degree

  • Ph.D.(Mathematical Sciences)

Academic & Professional Experience

  • 2012.04
    -
    Now

    Wakayama University

  • 2007.04
    -
    2012.03

    Wakayama University

  • 1998.04
    -
    2007.03

    Wakayama University

  • 1996.04
    -
    1998.03

    Wakayama University

Association Memberships

  • 日本数学会

Research Areas

  • Natural sciences / Algebra

Classes (including Experimental Classes, Seminars, Graduation Thesis Guidance, Graduation Research, and Topical Research)

  • 2023   Seminar of Mathematical EducationC4   Specialized Subjects

  • 2023   Seminar of Mathematical EducationC3   Specialized Subjects

  • 2023   Seminar of Mathematical EducationC2   Specialized Subjects

  • 2023   Seminar of Mathematical EducationC1   Specialized Subjects

  • 2023   The world of integers   Specialized Subjects

  • 2023   Research on Teaching Materials in Arithmetics   Specialized Subjects

  • 2023   Basic Exercise of Mathematics   Specialized Subjects

  • 2023   Introduction to Group Theory   Specialized Subjects

  • 2023   Introduction to Computers   Specialized Subjects

  • 2022   Seminar of Mathematical EducationC4   Specialized Subjects

  • 2022   Seminar of Mathematical EducationC3   Specialized Subjects

  • 2022   Seminar of Mathematical Education   Specialized Subjects

  • 2022   Seminar of Mathematical EducationC1   Specialized Subjects

  • 2022   Introduction to Group Theory   Specialized Subjects

  • 2022   The world of integers   Specialized Subjects

  • 2022   Research on Teaching Materials in Arithmetics   Specialized Subjects

  • 2022   Basic Exercise of Mathematics   Specialized Subjects

  • 2022   Introduction to Computers   Specialized Subjects

  • 2022   Elementary Theory of Numbers   Specialized Subjects

  • 2021   Seminar of Mathmatical Education A   Specialized Subjects

  • 2021   Seminar of Mathmatical Education B   Specialized Subjects

  • 2021   Research on Teaching Materials in Arithmetics   Specialized Subjects

  • 2021   Seminar of Mathmatical Education   Specialized Subjects

  • 2021   Seminar of Mathematical Education C   Specialized Subjects

  • 2021   Seminar of Mathematical Education D   Specialized Subjects

  • 2021   Elementary Theory of Numbers   Specialized Subjects

  • 2021   Introduction to Computers   Specialized Subjects

  • 2021   Basic Exercise of Mathematics   Specialized Subjects

  • 2021   The world of integers   Specialized Subjects

  • 2021   Introduction to Group Theory   Specialized Subjects

  • 2020   Seminar of Mathematical Education D   Specialized Subjects

  • 2020   Seminar of Mathematical Education C   Specialized Subjects

  • 2020   Introduction to Group Theory   Specialized Subjects

  • 2020   Seminar of Mathmatical Education   Specialized Subjects

  • 2020   The world of integers   Specialized Subjects

  • 2020   Research on Teaching Materials in Arithmetics   Specialized Subjects

  • 2020   Basic Exercise of Mathematics   Specialized Subjects

  • 2020   Seminar of Mathmatical Education B   Specialized Subjects

  • 2020   Seminar of Mathmatical Education A   Specialized Subjects

  • 2020   Introduction to Computers   Specialized Subjects

  • 2020   Elementary Theory of Numbers   Specialized Subjects

  • 2019   Seminar of Mathematical Education D   Specialized Subjects

  • 2019   Seminar of Mathematical Education C   Specialized Subjects

  • 2019   Introduction to Group Theory   Specialized Subjects

  • 2019   Seminar of Mathmatical Education   Specialized Subjects

  • 2019   The world of integers   Specialized Subjects

  • 2019   Research on Teaching Materials in Arithmetics   Specialized Subjects

  • 2019   Basic Exercise of Mathematics   Specialized Subjects

  • 2019   Seminar of Mathmatical Education B   Specialized Subjects

  • 2019   Seminar of Mathmatical Education A   Specialized Subjects

  • 2019   Introduction to Computers   Specialized Subjects

  • 2019   Elementary Theory of Numbers   Specialized Subjects

  • 2018   Introduction to Group Theory   Specialized Subjects

  • 2018   The world of integers   Specialized Subjects

  • 2018   Research on Teaching Materials in Arithmetics   Specialized Subjects

  • 2018   Basic Exercise of Mathematics   Specialized Subjects

  • 2018   Seminar of Mathmatical Education B   Specialized Subjects

  • 2018   Seminar of Mathmatical Education A   Specialized Subjects

  • 2018   Introduction to Computers   Specialized Subjects

  • 2018   Elementary Theory of Numbers   Specialized Subjects

  • 2017   Basic Exercise of Mathematics   Specialized Subjects

  • 2017   Seminar of Mathmatical Education B   Specialized Subjects

  • 2017   Seminar of Mathmatical Education A   Specialized Subjects

  • 2017   Symmetry in Nature(Group Theory) of Sociology   Specialized Subjects

  • 2017   Discrete Mathematics   Specialized Subjects

  • 2017   Introduction to Computers   Specialized Subjects

  • 2017   Elementary Theory of Numbers   Specialized Subjects

  • 2016   Seminar of Mathmatical Education B   Specialized Subjects

  • 2016   Seminar of Mathmatical Education A   Specialized Subjects

  • 2016   Introduction to Computers   Specialized Subjects

  • 2016   Seminar of Mathmatical Education B   Specialized Subjects

  • 2016   Seminar of Mathmatical Education A   Specialized Subjects

  • 2016   Introduction to Computers   Specialized Subjects

  • 2016   Basic Exercise of Mathematics   Specialized Subjects

  • 2016   Symmetry in Nature(Group Theory) of Sociology   Specialized Subjects

  • 2016   Discrete Mathematics   Specialized Subjects

  • 2016   Elementary Theory of Numbers   Specialized Subjects

  • 2015   Introduction to Computers   Specialized Subjects

  • 2015   Seminar of Mathmatical Education A   Specialized Subjects

  • 2015   Elementary Theory of Numbers   Specialized Subjects

  • 2015   Discrete Mathematics   Specialized Subjects

  • 2015   Seminar of Mathmatical Education B   Specialized Subjects

  • 2015   Basic Exercise of Mathematics   Specialized Subjects

  • 2015   Symmetry in Nature(Group Theory) of Sociology   Specialized Subjects

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Classes

  • 2020   Research Work   Master's Course

  • 2019   Advanced Seminar in Algebra B   Master's Course

  • 2019   Advanced Algebra B   Master's Course

  • 2019   Research Work   Master's Course

  • 2018   Advanced Seminar in Algebra B   Master's Course

  • 2018   Advanced Algebra B   Master's Course

  • 2017   Research Work   Master's Course

  • 2016   Advanced Seminar in Algebra B   Master's Course

  • 2016   Advanced Algebra B   Master's Course

  • 2015   Research Work  

  • 2015   Lectures on Mathematical education  

  • 2015   Advanced Seminar in Algebra Ⅱ  

  • 2015   Advanced Algebra Ⅱ  

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Research Interests

  • Algebraic Combinatorics

Published Papers

  • Jeśmanowicz’ conjecture for non-primitive Pythagorean triples

    Hidetaka Kitayama, Hiroyuki Tagawa, Keiichi Urahashi

    Periodica Mathematica Hungarica ( Springer Science and Business Media LLC )  86 ( 2 ) 442 - 453   2023.06  [Refereed]

    DOI

  • A QUADRATIC FORMULA FOR BASIC HYPERGEOMETRIC SERIES RELATED TO ASKEY-WILSON POLYNOMIALS

    Victor J. W. Guo, Masao Ishikawa, Hiroyuki Tagawa, Jiang Zeng

    PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY ( AMER MATHEMATICAL SOC )  143 ( 5 ) 2003 - 2015   2015.05  [Refereed]

    　View Summary

    We prove a general quadratic formula for basic hypergeometric series, from which simple proofs of several recent determinant and Pfaffian formulas are obtained. A special case of the quadratic formula is actually related to a Gram determinant formula for Askey-Wilson polynomials. We also show how to derive a recent double-sum formula for the moments of Askey-Wilson polynomials from Newton's interpolation formula.

    DOI

  • Pfaffian decomposition and a Pfaffian analogue of q-Catalan Hankel determinants

    Masao Ishikawa, Hiroyuki Tagawa, Jiang Zeng

    JOURNAL OF COMBINATORIAL THEORY SERIES A ( ACADEMIC PRESS INC ELSEVIER SCIENCE )  120 ( 6 ) 1263 - 1284   2013.08  [Refereed]

    　View Summary

    Motivated by the Hankel determinant evaluation of moment sequences, we study an analogous Pfaffian evaluation. We prove an LU-decomposition analogue for skew-symmetric matrices, called Pfaffian decomposition. We then apply this formula to evaluate Pfaffians related to some moment sequences of classical orthogonal polynomials. In particular we obtain a product formula for a kind of q-Catalan Pfaffians. We also establish a connection between our Pfaffian formulas and certain weighted enumeration of shifted reverse plane partitions. (C) 2013 Elsevier Inc. All rights reserved.

    DOI

  • A generalization of Mehta-Wang determinant and Askey-Wilson polynomials

    Masao Ishikawa, Hiroyuki Tagawa, Jiang Zeng

    Proceedings of the 25th International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC'13),(Discrete Math. Theor. Comput. Sci. Proc., AS)     719 - 730   2013  [Refereed]

  • A q-analogue of Catalan Hankel determinants

    Masao Ishikawa, Hiroyuki Tagawa, Jiang Zeng

    RIMS Kokyuroku Bessatsu B11, New Trends in Combinatorial Representation Theory ( Kyoto University )  11   19 - 41   2009  [Refereed]

  • Schur Function Identities and Hook Length Posets

    Masao Ishikawa, Hiroyuki Tagawa

    Proceedings of the 19th International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC'07)     2007.06  [Refereed]

  • Generalizations of Cauchy's determinant and Schur's pfaffian

    M Ishikawa, S Okada, H Tagawa, J Zeng

    ADVANCES IN APPLIED MATHEMATICS ( ACADEMIC PRESS INC ELSEVIER SCIENCE )  36 ( 3 ) 251 - 287   2006.03  [Refereed]

    　View Summary

    We present several identities of Cauchy-type determinants and Schur-type Pfaffians involving generalized Vandermonde determinants, which generalize Cauchy's determinant det(1 /(x(i) + y(j))) and Schur's Pfaffian Pf((x(j) - x(i))/(x(j) + x(i))). Some special cases of these identities are given by S. Okada and T. Sundquist. As an application, we give a relation for the Littlewood-Richard son coefficients involving a rectangular partition. (c) 2005 Elsevier Inc. All rights reserved.

    DOI

  • Generalizations of Cauchy's Determinant and Schur's Pfaffian

    Masao Ishikawa, Soichi Okada, Hiroyuki Tagawa, Jiang Zeng

    Proceedings of the 17th International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC'05)     231 - 242   2005.06  [Refereed]

  • A Characterization of the Simply-Laced FC-Finite Coxeter Groups

    Manabu Hagiwara, Masao Ishikawa, Hiroyuki Tagawa

    Annals of Combinatorics   8   177 - 196   2004  [Refereed]

  • Generalized (P, omega)-partitions and generating functions for trees

    Arima, I, H Tagawa

    JOURNAL OF COMBINATORIAL THEORY SERIES A ( ACADEMIC PRESS INC ELSEVIER SCIENCE )  103 ( 1 ) 137 - 150   2003.07  [Refereed]

    　View Summary

    We introduce (P, R)-partitions as a generalization of the (P,omega)-partitions of Stanley. When P is a Gaussian poset the generating function for P-partitions with largest part at most n factors as Pixis an element ofP 1-q(g(x)+n)/1-q(g(x)) for certain integers g(x). Although trees are not in general Gaussian posets, we show that if P is a tree then R can be chosen so that the generating function for (P, R)-partitions has a similar factorization. (C) 2003 Elsevier Science (USA). All rights reserved.

    DOI

  • Some properties of inverse weighted parabolic Kazhdan-Lusztig polynomials

    H Tagawa

    JOURNAL OF ALGEBRA ( ACADEMIC PRESS INC )  239 ( 1 ) 298 - 326   2001.05  [Refereed]

    DOI

  • A recursion formula of the weighted parabolic Kazhdan-Lusztig polynomials

    H Tagawa

    COMBINATORIAL METHODS IN REPRESENTATION THEORY ( KINOKUNIYA CO LTD )  28   373 - 389   2000  [Refereed]

    　View Summary

    In this article, we give a recursion formula of the weighted parabolic Kazhdan-Lusztig polynomials and describe a relationship between those polynomials and weighted Kazhdan-Lusztig polynomials introduced by G.Lusztig ([4]).

  • A construction of weighted parabolic Kazhdan-Lusztig polynomials

    H Tagawa

    JOURNAL OF ALGEBRA ( ACADEMIC PRESS INC )  216 ( 2 ) 566 - 599   1999.06  [Refereed]

  • Kazhdan-Lusztig polynomials of parabolic type

    H Tagawa

    JOURNAL OF ALGEBRA ( ACADEMIC PRESS INC )  200 ( 1 ) 258 - 278   1998.02  [Refereed]

    DOI

  • ON THE NON-NEGATIVITY OF THE FIRST COEFFICIENT OF KAZHDAN-LUSZTIG POLYNOMIALS

    H TAGAWA

    JOURNAL OF ALGEBRA ( ACADEMIC PRESS INC JNL-COMP SUBSCRIPTIONS )  177 ( 3 ) 698 - 707   1995.11  [Refereed]

  • A DECOMPOSITION OF R-POLYNOMIALS AND KAZHDAN-LUSZTIG POLYNOMIALS

    H TAGAWA

    PROCEEDINGS OF THE JAPAN ACADEMY SERIES A-MATHEMATICAL SCIENCES ( JAPAN ACAD )  71 ( 6 ) 107 - 108   1995.06  [Refereed]

  • On the maximum value of the first coefficients of Kazhdan-Lusztig polynomials for symmetric groups

    Hiroyuki Tagawa

    Journal of Mathematical Sciences, The University of Tokyo ( The University of Tokyo )  1 ( 2 ) 461 - 469   1994  [Refereed]

    　View Summary

    In this article, we show that max$\{c^-(w);w \in \frak S_n\} = [n^2/4]$, where $c^-(w)$ is the number of elements covered by $w \in \frak S_n$ in the Bruhat order. Using this result, we can see that the maximum value of the first coefficients of Kazhdan-Lusztig polynomials for $\frak S_n$ equals $[n^2/4]- n + 1$.

  • On the first coefficients in q of the Kazhdan-Lusztig polynomials

    Hiroyuki Tagawa

    Tokyo Journal of Mathematics   17 ( 1 ) 219 - 228   1994  [Refereed]

    DOI

  • q-Analogues of determinants and symmetric chain decompositions

    Hiroyuki Tagawa

    Tokyo Journal of Mathematics   16 ( 2 ) 311 - 320   1993  [Refereed]

    　View Summary

    We introduce multivariable q-analogues of the determinant and show a sufficient condition for an interval of the symmetric group to have a symmetric chain decomposition in the Bruhat order by using the expansion formulas. © 1993, International Academic Printing Co. Ltd., All rights reserved.

    DOI

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Misc

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Research Exchange

  • 石取りゲームについての共同研究

    2023.04
    -
    Now
     

    　Joint research

  • Jesmanowicz' conjecture についての共同研究

    2021.04
    -
    Now
     

    　Joint research

KAKENHI

  • 行列と超幾何級数に関連した代数的組合せ論とその周辺

    2016.04
    -
    2021.03
     

    Grant-in-Aid for Scientific Research(C)  Principal investigator

  • リーフポセットに関連した表現論的組合せ論とその周辺

    2011.04
    -
    2016.03
     

    Grant-in-Aid for Scientific Research(C)  Principal investigator

  • hook length posetの組合せ論的及び表現論的研究

    2003.04
    -
    2007.03
     

    Grant-in-Aid for Scientific Research(C)  Principal investigator

Instructor for open lecture, peer review for academic journal, media appearances, etc.

  • 教育論文審査

    2021.09.16
    -
    2021.10.08

    岸和田市教育委員会

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    審査

    教育論文の書面審査。

  • 知の冒険旅行

    2019.04

    その他

    　View Details

    小・中・高校生を対象とした学部体験入学・出張講座等

    １５パズルに潜む数学（９０分授業を1回、和歌山大学教育学部）,日付:9月19日

Course for renewal of teaching license, teacher-librarian course, etc. (contracted business）

  • 2021  【選択】整数に潜む数学の探究(教員免許状更新講習)

  • 2020  【選択】整数に潜む数学の探究(教員免許状更新講習)

  • 2019  整数に潜む数学の探究（免許更新講習）

  • 2018  整数に潜む数学の探究（免許更新講習）

  • 2017  整数に潜む数学の探究（免許更新講習）

  • 2016  整数に潜む数学の探究（免許更新講習）

  • 2015  整数に潜む数学の探究（免許更新講習）

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Committee member history in academic associations, government agencies, municipalities, etc.

  • 和歌山県ゴールデンキッズ発掘プロジェクト実行委員会委員

    2023.04.01
    -
    2024.03.31
     

    和歌山県教育委員会

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    学協会、政府、自治体等の公的委員

    ゴールデンキッズ発掘プロジェクトの年間計画の決定・予算案決定等

Other Social Activities

  • 和歌山市教育委員会と和歌山大学教育学部との連携協力のための運営協議会

    2023.04
    -
    2024.03

    その他

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    社会との連携を推進する活動

    表記目的を遂行するための運営協議会に出席した。