17 citations · 39 across the 18 of their papers we have counts for
7 papers · 1 filter
Group Permanents of Abelian -Groups and Young Diagrams
Naoya Yamaguchi, Yuka Yamaguchi
We study the number $\Nu(\Per(G_λ))$ of distinct monomials with nonzero coefficients in the group permanent of an abelian -group associated with a partition of a posit…
Group Determinants and Invariant Rings
Yuka Yamaguchi, Naoya Yamaguchi
In the study of group determinants, Frobenius introduced certain partial differential operators. This paper presents several results concerning the invariant rings derived from the…
First and Second Fundamental Theorems for Invariant Rings Generated by Circulant Determinants
Naoya Yamaguchi, Hiroyuki Ochiai, Yuka Yamaguchi
In this paper, we give the first and second fundamental theorems of invariant theory for certain invariant rings whose generators are expressed by circulant determinants.
Principal Specialization of Monomial Symmetric Polynomials and Group Determinants of Cyclic Groups
Naoya Yamaguchi, Yuka Yamaguchi, Genki Shibukawa
In this paper, we study the principal specialization of monomial symmetric polynomials and investigate the special values of these polynomials at \[ ζ_{(n,k)} := ( 1, ζ_n, ζ_n^2, \…
Generalized Dedekind's theorem and its application to integer group determinants
Naoya Yamaguchi, Yuka Yamaguchi
In this paper, we give a refinement of a generalized Dedekind's theorem. In addition, we show that all possible values of integer group determinants of any group are also possible…
Remark on Laquer's theorem for circulant determinants
Naoya Yamaguchi, Yuka Yamaguchi
Olga Taussky-Todd suggested the problem of determining the possible values of integer circulant determinants. To solve a special case of the problem, Laquer gave a factorization of…
Generalized group determinant gives a necessary and sufficient condition for a subset of a finite group to be a subgroup
Naoya Yamaguchi, Yuka Yamaguchi
We generalize the concept of the group determinant and prove a necessary and sufficient novel condition for a subset to be a subgroup. This development is based on the group determ…