The quantities c（G）, q（G） and p（G） for finite groups were defined by H. Behravesh. In this article, these quantities for the alternating group An and the symmetric group Sn are calculated. It is shown that c（G...The quantities c（G）, q（G） and p（G） for finite groups were defined by H. Behravesh. In this article, these quantities for the alternating group An and the symmetric group Sn are calculated. It is shown that c（G） = q（G） = p（G） = n,when G = An or Sn.展开更多
Pfaffians of matrices with entries z[i, j]/（xi ＋ xj）, or determinants of matrices with entries z[i, j]/（xi - xj）, where the antisymmetrical indeterminates z[i, j] satisfy the Pliicker relations, can be identified...Pfaffians of matrices with entries z[i, j]/（xi ＋ xj）, or determinants of matrices with entries z[i, j]/（xi - xj）, where the antisymmetrical indeterminates z[i, j] satisfy the Pliicker relations, can be identified with a trace in an irreducible representation of a product of two symmetric groups. Using Young＇s orthogonal bases, one can write explicit expressions of such Pfaffians and determinants, and recover in particular the evaluation of Pfaffians which appeared in the recent literature.展开更多
I.INTRODUCTION There are two different representations for symmetric group: the ordinary representation and the spin representation. As for the characters of spin irreducible representations(irreps), A. O. Morris give...I.INTRODUCTION There are two different representations for symmetric group: the ordinary representation and the spin representation. As for the characters of spin irreducible representations(irreps), A. O. Morris gives the character tables of 4≤n≤13 with the method of Q functions.展开更多
It is shown that in Lagrangian numerical differentiation formulas, the coefficients are explicitly expressed by means of cycle indicator polynomials of symmetric group. Moreover, asymptotic expansions of the remainder...It is shown that in Lagrangian numerical differentiation formulas, the coefficients are explicitly expressed by means of cycle indicator polynomials of symmetric group. Moreover, asymptotic expansions of the remainders are also explicitly represented as a fixed number of interpolation nodes approaching infinitely to the point at which the derivative is evaluated. This implies that complete explicit formulas for local Lagrangian numerical differentiation can be obtained.展开更多
文摘The quantities c（G）, q（G） and p（G） for finite groups were defined by H. Behravesh. In this article, these quantities for the alternating group An and the symmetric group Sn are calculated. It is shown that c（G） = q（G） = p（G） = n,when G = An or Sn.
文摘Pfaffians of matrices with entries z[i, j]/（xi ＋ xj）, or determinants of matrices with entries z[i, j]/（xi - xj）, where the antisymmetrical indeterminates z[i, j] satisfy the Pliicker relations, can be identified with a trace in an irreducible representation of a product of two symmetric groups. Using Young＇s orthogonal bases, one can write explicit expressions of such Pfaffians and determinants, and recover in particular the evaluation of Pfaffians which appeared in the recent literature.
文摘I.INTRODUCTION There are two different representations for symmetric group: the ordinary representation and the spin representation. As for the characters of spin irreducible representations(irreps), A. O. Morris gives the character tables of 4≤n≤13 with the method of Q functions.
基金supported in part by the National Natural Science Foundation of China(Grant No.10471128)
文摘It is shown that in Lagrangian numerical differentiation formulas, the coefficients are explicitly expressed by means of cycle indicator polynomials of symmetric group. Moreover, asymptotic expansions of the remainders are also explicitly represented as a fixed number of interpolation nodes approaching infinitely to the point at which the derivative is evaluated. This implies that complete explicit formulas for local Lagrangian numerical differentiation can be obtained.
