Takao Komatsu 研究室

主宰者：Takao Komatsu

東京工業大学

AI 要約（直近 5 年の研究成果）

小松研究室は、整数論における古典的な問題を新しい視点から拡張・一般化する研究を行っています。特に、フロベニウス数に関する研究が中核をなしており、与えられた正の整数の非負整数係数による線形結合で表現できない最大の整数を求める問題に取り組んでいます。従来は特殊な場合にしか明示的な公式が知られていませんでしたが、本研究室では数列や多項式に関連した三つ組などの具体的なクラスに対して、フロベニウス数を求める一般的な公式を導出しています。同時に、この古典的な問題を一般化した「p-フロベニウス数」という概念を導入し、線形方程式の非負整数解の個数が指定された回数以下になる最大の整数を特性化する研究を展開しています。この拡張により、数値半群の理論も新たな角度から検討されています。さらに、特殊な数（調和数、多重ゼータ値、スターリング数など）の算術的性質や組合せ的性質を調べる研究も並行して進められています。これらの数に関する多項式や恒等式、除割性性質といった基本的な性質を明らかにすることで、整数論全体の理解を深めるとともに、フロベニウス問題などの応用的課題へとつなげています。

※ AI（Claude）が、公開されている論文要旨から研究の問い・手法・主要な発見を事実情報として抽出・再構成して自動生成しています。誤りを含む可能性があるため、正確性は研究室公式情報でご確認ください。

外部リンク

研究成果（57 件）

[2026] Some Explicit Values of a q-Multiple t-Function of Level 3 at Roots of Unity
DOI: https://doi.org/10.1007/s00025-026-02675-8
[2025] Analytical aspects of a q, r-analogue of poly-Stirling numbers of both kinds
DOI: https://doi.org/10.1007/s00010-024-01135-4
[2025] Some explicit values of an alternative q -multiple zeta function at roots of unity
DOI: https://doi.org/10.1093/jigpal/jzaf075
[2025] Some explicit values of a q-multiple t-function at roots of unity
DOI: https://doi.org/10.1007/s00010-025-01235-9
[2025] Fibonacci determinants. II
DOI: https://doi.org/10.1007/s10986-025-09691-1
[2025] Polynomial Identities for Binomial Sums of Harmonic Numbers of Higher Order
DOI: https://doi.org/10.3390/math13020321
[2025] Special Values of a q-Multiple t-Function of General Level at the Roots of Unity
DOI: https://doi.org/10.1007/s00009-025-02993-1
[2025] Congruence properties of Lehmer-Euler numbers
DOI: https://doi.org/10.1007/s00010-024-01150-5
[2025] Explicit values of a q-multiple zeta-star function at roots of unity
DOI: https://doi.org/10.1051/ita/2025005
[2025] Some explicit forms of special values of an alternating q-multiple t-function of general level at roots of unity
DOI: https://doi.org/10.1007/s11139-025-01150-2

続きを表示（残り 47 件）

[2025] Frobenius numbers associated with Diophantine triples of $$x^2+3 y^2=z^3$$
DOI: https://doi.org/10.1007/s13398-025-01725-0
[2025] Some explicit values of a q-multiple zeta function at roots of unity
DOI: https://doi.org/10.1016/j.jmaa.2025.130065
[2024] Frobenius Numbers Associated with Diophantine Triples of x2-y2=zr
DOI: https://doi.org/10.3390/sym16070855
[2024] The p-Frobenius Number for the Triple of the Generalized Star Numbers
DOI: https://doi.org/10.3390/sym16081090
[2024] Bernoulli numbers with level 2
DOI: https://doi.org/10.1007/s00010-024-01089-7
[2024] On a Zaremba’s Conjecture for Powers
DOI: https://doi.org/10.5644/sjm.01.1.02
[2024] More on Hurwitz and Tasoev Continued Fractions
DOI: https://doi.org/10.5644/sjm.04.2.02
[2024] FROBENIUS NUMBERS ASSOCIATED WITH DIOPHANTINE TRIPLES OF $x^2+y^2=z^3$
DOI: https://doi.org/10.1017/s0004972724000960
[2024] On the determination of p-Frobenius and related numbers using the p-Apéry set
DOI: https://doi.org/10.1007/s13398-024-01556-5
[2024] A generalization of Mneimneh's binomial sum of harmonic numbers
DOI: https://doi.org/10.1016/j.disc.2024.113945
[2024] The p -Frobenius number for the triple of certain quadratic numbers
DOI: https://doi.org/10.1093/jigpal/jzae125
[2024] The Frobenius number for shifted geometric sequences associated with the number of solutions
DOI: https://doi.org/10.5486/pmd.2024.9796
[2024] p-Numerical Semigroups of Triples from the Three-Term Recurrence Relations
DOI: https://doi.org/10.3390/axioms13090608
[2024] p-Numerical semigroups with p-symmetric properties, II
DOI: https://doi.org/10.1142/s0219498826500258
[2024] On arithmetical properties of degenerate Cauchy polynomials and numbers
DOI: https://doi.org/10.15672/hujms.1354679
[2023] Summation formulas of hyperharmonic numbers with their generalizations
DOI: https://doi.org/10.1007/s13370-023-01131-y
[2023] The p-Frobenius Problems for the Sequence of Generalized Repunits
DOI: https://doi.org/10.1007/s00025-023-02055-6
[2023] The p-Numerical Semigroup of the Triple of Arithmetic Progressions
DOI: https://doi.org/10.3390/sym15071328
[2023] On q-generalized (r, s)-Stirling numbers
DOI: https://doi.org/10.1007/s00010-023-00997-4
[2023] Continued Fraction Expansions Towards Zaremba’s Conjecture
DOI: https://doi.org/10.1080/10586458.2023.2293285
[2023] p-Numerical semigroups with p-symmetric properties
DOI: https://doi.org/10.1142/s0219498824502165
[2023] p-Numerical Semigroups of Generalized Fibonacci Triples
DOI: https://doi.org/10.3390/sym15040852
[2023] Poly-Cauchy Numbers with Higher Level
DOI: https://doi.org/10.3390/sym15020354
[2023] The Frobenius Number for Jacobsthal Triples Associated with Number of Solutions
DOI: https://doi.org/10.3390/axioms12020098
[2023] The Frobenius number associated with the number of representations for sequences of repunits
DOI: https://doi.org/10.5802/crmath.394
[2022] WEIGHTED SYLVESTER SUMS ON THE FROBENIUS SET IN MORE VARIABLES
DOI: https://doi.org/10.2206/kyushujm.76.163
[2022] A parametric type of Cauchy polynomials
DOI: https://doi.org/10.18514/mmn.2022.3652
[2022] Stirling numbers with level $2$ and poly-Bernoulli numbers with level $2$
DOI: https://doi.org/10.5486/pmd.2022.9177
[2022] On s-Stirling transform and poly-Cauchy numbers of the second kind with level 2
DOI: https://doi.org/10.1007/s00010-022-00931-0
[2022] Convolution identities of poly-Cauchy numbers with level 2
DOI: https://doi.org/10.4171/rsmup/106
[2022] Recurrence Relations of Poly-Cauchy Numbers by the r-Stirling Transform
DOI: https://doi.org/10.1007/s00009-021-01960-w
[2022] The Frobenius Number for Sequences of Triangular Numbers Associated with Number of Solutions
DOI: https://doi.org/10.1007/s00026-022-00594-3
[2022] A parametric type of Bernoulli polynomials with higher level
DOI: https://doi.org/10.15421/242205
[2022] A q, r -analogue for the Stirling numbers of the second kind of Coxeter groups of type B
DOI: https://doi.org/10.2478/puma-2022-0003
[2022] Sylvester power and weighted sums on the Frobenius set in arithmetic progression
DOI: https://doi.org/10.1016/j.dam.2022.03.011
[2022] The $ p $-Frobenius and $ p $-Sylvester numbers for Fibonacci and Lucas triplets
DOI: https://doi.org/10.3934/mbe.2023162
[2021] A Parametric Type of Cauchy Polynomials with Higher Level
DOI: https://doi.org/10.3390/axioms10030207
[2021] Several formulas for Bernoulli numbers and polynomials
DOI: https://doi.org/10.3934/amc.2021006
[2021] Several Continued Fraction Expansions of Generalized Cauchy Numbers
DOI: https://doi.org/10.1007/s40840-021-01074-2
[2021] Weighted Sylvester sums on the Frobenius set
DOI: https://doi.org/10.33232/bims.0087.35.44
[2021] Cameron’s operator in terms of determinants and hypergeometric numbers
DOI: https://doi.org/10.1007/s40590-021-00401-8
[2021] Asymmetric circular graph with Hosoya index and negative continued fractions
DOI: https://doi.org/10.15330/cmp.13.3.608-618
[2021] On hypergeometric Cauchy numbers of higher grade
DOI: https://doi.org/10.3934/math.2021390
[2021] A Combinatorial Approach to the Stirling Numbers of the First Kind with Higher Level
DOI: https://doi.org/10.1556/012.2021.58.3.1500
[2021] Direct and inverse problems for restricted signed sumsets in integers
DOI: https://doi.org/10.55016/ojs/cdm.v16i1.69407
[2021] Summation formulas of q-hyperharmonic numbers
DOI: https://doi.org/10.1007/s13370-021-00891-9
[2021] A Combinatorial Approach to the Generalized Central Factorial Numbers
DOI: https://doi.org/10.1007/s00009-021-01830-5

科研費（0 件）

まだデータがありません（KAKEN 取り込み後に表示）。

所属学会・役職（0 件）

まだデータがありません（学会データ連携後に表示）。

AI 要約（直近 5 年の研究成果）

外部リンク

関連研究室(8 件)

研究成果（57 件）

科研費（0 件）

所属学会・役職（0 件）