FullText URL mjou_064_153_186.pdf
Author Nishiyama, Yuta|
Abstract In this article, we introduce some identities obtained from the inner products of some symmetric polynomials including the Macdonald polynomials. These identities are obtained not only from the inner products, but also by constructing certain bijections. The bijections are constructed through transforming the Young diagrams of partitions.
Keywords Macdonald polynomials Young diagram bijective proof
Published Date 2022-01
Publication Title Mathematical Journal of Okayama University
Volume volume64
Issue issue1
Publisher Department of Mathematics, Faculty of Science, Okayama University
Start Page 153
End Page 186
ISSN 0030-1566
NCID AA00723502
Content Type Journal Article
language 英語
Copyright Holders Copyright ©2022 by the Editorial Board of Mathematical Journal of Okayama University
FullText URL mjou_064_187_190.pdf
Author Puthenpurakal, Tony J. |
Abstract Let K be a field and consider the standard grading on A = K[X<sub>1</sub>, ... ,X<sub>d</sub>]. Let I, J be monomial ideals in A. Let I<sub>n</sub>(J) = (I<sup>n</sup> : J<sup>&infin;</sup>) be the n<sup>th</sup> symbolic power of I with respect to J. It is easy to see that the function f<sup>I</sup> <sub>J</sub> (n) = e<sub>0</sub>(I<sub>n</sub>(J)/I<sup>n</sup>) is of quasi-polynomial type, say of period g and degree c. For n ≫ 0 say<br> <br> f<sup>I</sup><sub>J</sub> (n) = a<sub>c</sub>(n)n<sup>c</sup> + a<sub>c−1</sub>(n)n<sup>c−1</sup> + lower terms,<br> <br> where for i = 0, ... , c, a<sub>i</sub> : N → Q are periodic functions of period g and a<sub>c</sub> &ne;0. In [4, 2.4] we (together with Herzog and Verma) proved that dim I<sub>n</sub>(J)/I<sup>n</sup> is constant for n ≫ 0 and a<sub>c</sub>(−) is a constant. In this paper we prove that if I is generated by some elements of the same degree and height I ≥ 2 then a<sub>c−1</sub>(−) is also a constant.
Keywords quasi-polynomials monomial ideals symbolic powers
Published Date 2022-01
Publication Title Mathematical Journal of Okayama University
Volume volume64
Issue issue1
Publisher Department of Mathematics, Faculty of Science, Okayama University
Start Page 187
End Page 190
ISSN 0030-1566
NCID AA00723502
Content Type Journal Article
language 英語
Copyright Holders Copyright ©2022 by the Editorial Board of Mathematical Journal of Okayama University
FullText URL mjou_064_191_213.pdf
Author Suzuki, Takeshi| Toyosawa, Yoshitaka|
Abstract We present a conjectural hook formula concerning the number of the standard tableaux on "cylindric" skew diagrams. Our formula can be seen as an extension of Naruse's hook formula for skew diagrams. Moreover, we prove our conjecture in some special cases.
Published Date 2022-01
Publication Title Mathematical Journal of Okayama University
Volume volume64
Issue issue1
Publisher Department of Mathematics, Faculty of Science, Okayama University
Start Page 191
End Page 213
ISSN 0030-1566
NCID AA00723502
Content Type Journal Article
language 英語
Copyright Holders Copyright ©2022 by the Editorial Board of Mathematical Journal of Okayama University
FullText URL mjou_064_215_225.pdf
Author Hyodo, Fumitake|
Abstract This paper focuses on the theory of the Hecke rings associated with the general linear groups originally studied by Hecke and Shimura et al., and moreover generalizes its notions to Hecke rings associated with the automorphism groups of certain algebras. Then, in the case of the Heisenberg Lie algebra, we show an analog of the classical theory.
Keywords Hecke rings noncommutative rings
Published Date 2022-01
Publication Title Mathematical Journal of Okayama University
Volume volume64
Issue issue1
Publisher Department of Mathematics, Faculty of Science, Okayama University
Start Page 215
End Page 225
ISSN 0030-1566
NCID AA00723502
Content Type Journal Article
language 英語
Copyright Holders Copyright ©2022 by the Editorial Board of Mathematical Journal of Okayama University