• Title, Summary, Keyword: multiplicity

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THE HILBERT-KUNZ MULTIPLICITY OF TWO-DIMENSIONAL TORIC RINGS

  • Choi, Sang-Ki;Hong, Seok-Young
    • Journal of the Korean Mathematical Society
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    • v.40 no.2
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    • pp.169-177
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    • 2003
  • Recently, K. Watanabe Showed that the Hilbert-Kunz multiplicity of a toric ring is a rational number. In this paper we give an explicit formula to compute the Hilbert-Kunz multiplicity of two-dimensional toric rings. This formula also shows that the Hilbert-Kunz multiplicity of a two-dimensional non-regular toric ring is at least 3/2.

MULTIPLICITY-FREE ACTIONS OF THE ALTERNATING GROUPS

  • Balmaceda, Jose Maria P.
    • Journal of the Korean Mathematical Society
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    • v.34 no.2
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    • pp.453-467
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    • 1997
  • A transitive permutation representation of a group G is said to be multiplicity-free if all of its irreducible constituents are distinct. The character corresponding to the action is called the permutation character, given by $(1_H)^G$, where H is the stabilizer of a point. Multiplicity-free permutation characters are of interest in the study of centralizer algebras and distance-transitive graphs, and all finite simple groups are known to have such characters. In this article, we extend to the alternating groups the result of J. Saxl who determined the multiplicity-free permutation representations of the symmetric groups. We classify all subgroups H for which $(1_H)^An, n > 18$, is multiplicity-free.

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ON A CHANGE OF RINGS FOR MIXED MULTIPLICITIES

  • Thanh, Truong Thi Hong;Viet, Duong Quoc
    • Bulletin of the Korean Mathematical Society
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    • v.57 no.5
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    • pp.1251-1258
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    • 2020
  • This paper establishes a formula changing the ring from a Noetherian local ring A of dimension d > 0 containing the residue field k to the polynomial ring in d variables k[X1, X2, …, Xd] for mixed multiplicities. And as consequences, we get a formula for the multiplicity of Rees rings and formulas for mixed multiplicities and the multiplicity of Rees rings of quotient rings of A by highest dimensional associated prime ideals of A.

A Study on the Multivariate Stratified Random Sampling with Multiplicity (중복수가 있는 다변량 층화임의추출에 관한 연구(층별로 독립인 경우의 배분문제))

  • Kim, Ho-Il
    • Journal of the Korean Data and Information Science Society
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    • v.10 no.1
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    • pp.79-89
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    • 1999
  • A counting rule that allows an element to be linked to more than one enumeration unit is called a multiplicity counting rule. Sample designs that use multiplicity counting rules are called network samples. Defining a network to be a set of observation units with a given linkage pattern, a network may be linked with more than one selection unit, and a single selection unit may be linked with more than one network. This paper considers allocation for multivariate stratified random sampling with multiplicity.

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MULTIPLICITY OF SOLUTIONS AND SOURCE TERMS IN A NONLINEAR PARABOLIC EQUATION UNDER DIRICHLET BOUNDARY CONDITION

  • Choi, Q-Heung;Jin, Zheng-Guo
    • Bulletin of the Korean Mathematical Society
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    • v.37 no.4
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    • pp.697-710
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    • 2000
  • We investigate the existence of solutions of the nonlinear heat equation under Dirichlet boundary conditions on $\Omega$ and periodic condition on the variable t, $Lu-D_tu$+g(u)=f(x, t). We also investigate a relation between multiplicity of solutions and the source terms of the equation.

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