Schur Functions in Statistics I. The Preservation Theorem
نویسندگان
چکیده
منابع مشابه
Thom polynomials and Schur functions I
We give the Thom polynomials for the singularities I2,2, and A3 associated with maps (C•, 0) → (C, 0) with parameter k ≥ 0. We give the Schur function expansions of these Thom polynomials. Moreover, for the singularities Ai (with any parameter k ≥ 0) we analyze the “first approximation” F (i) to the Thom polynomial. Our computations combine the characterization of Thom polynomials via the “meth...
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When N is a normal subgroup of G, can we reconstruct G from N and G/N? In general, no. For instance, the groups Z/(p2) and Z/(p) × Z/(p) (for prime p) are nonisomorphic, but each has a cyclic subgroup of order p and the quotient by it also has order p. As another example, the nonisomorphic groups Z/(2p) and Dp (for odd prime p) have a normal subgroup that is cyclic of order p, whose quotient is...
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Fix a rectangular Young diagram R, and consider all the products of Schur functions sλsλc , where λ and λ c run over all (unordered) pairs of partitions which are complementary with respect to R. Theorem: The self-complementary products, s λ where λ = λ, are linearly independent of all other sλsλc . Conjecture: The products sλsλc are all linearly independent.
متن کاملA generalization of a second irreducibility theorem of I. Schur
in which cases either f(x) is irreducible or f(x) is the product of two irreducible polynomials of equal degree. If |an| = n > 1, then for some choice of a1, . . . , an−1 ∈ Z and a0 = ±1, we have that f(x) is reducible. I. Schur (in [8]) obtained this result in the special case that an = ±1. Further results along the nature of Theorem 1 are also discussed in [6]. The purpose of this paper is to...
متن کاملA Generalization of an Irreducibility Theorem of I. Schur
is irreducible. Irreducibility here and throughout this paper refers to irreducibility over the rationals. Some condition, such as ja0j = janj = 1, on the integers aj is necessary; otherwise, the irreducibility of all polynomials of the form above would imply every polynomial inZ[x] is irreducible (which is clearly not the case). In this paper, we will mainly be interested in relaxing the condi...
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ژورنال
عنوان ژورنال: The Annals of Statistics
سال: 1977
ISSN: 0090-5364
DOI: 10.1214/aos/1176343792