Let f be a polynomial with coefficients in the ring O K of integers of a number field. Suppose that f induces a permutation on the residue fields O K /α for infinitely many nonzero prime ideals α of O K . Then Schur's conjecture, namely that f is a composition of linear and Dickson polynomials, has
β¦ LIBER β¦
Proof of a positivity conjecture on Schur functions
β Scribed by Chen, William Y.C.; Ren, Anne X.Y.; Yang, Arthur L.B.
- Book ID
- 118275968
- Publisher
- Elsevier Science
- Year
- 2013
- Tongue
- English
- Weight
- 124 KB
- Volume
- 120
- Category
- Article
- ISSN
- 0097-3165
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Throughout this paper, let R be a complete discrete valuation ring with the residue field k and the quotient field K, and Ξ an R-order in a semisimple K-algebra A [CR]. We assume that k is a finite field with q elements. For an A-module V of finite length, we denote by L Ξ (V ) the set of full Ξ-lat