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Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：Fast Numerical Evaluation of Generalized Todd Polynomials
广义托德多项式 的快速数值 评估
2023/4/23
Fast Numerical Evaluation of Generalized Todd Polynomials.
Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：Zeros of complete symmetric polynomials over finite fields
有限域 完全对称 多项式 零点
2023/4/13
Wan and Zhang have recently obtained a nontrivial lower bound for the number of zeros of complete symmetric polynomials over finite fields, and proposed a problem whether their bound can be improved. ...
We use the Pieri and Giambelli formulas of [BKT1, BKT3] and
the calculus of raising operators developed in [BKT2, T1] to prove a tableau
formula for the eta polynomials of [BKT3] and the Stanley sym...
SCHUBERT POLYNOMIALS AND ARAKELOV THEORY OF ORTHOGONAL FLAG VARIETIES
SCHUBERT POLYNOMIALS ARAKELOV THEORY
2015/12/17
We propose a theory of combinatorially explicit Schubert polynomials which represent the Schubert classes in the Borel presentation of the
cohomology ring of the orthogonal flag variety X = SON...
ORTHOGONAL POLYNOMIALS ON THE SIERPINSKI GASKET
Jacobi matrix Laplacian Sierpinski Gasket Orthogonal Polynomials Recursion Relation
2015/12/10
The construction of a Laplacian on a class of fractals which includes the Sierpinski gasket (SG) has given rise to an intensive research on analysis on fractals. For instance, a complete theory of pol...
SPLITTING FIELDS OF CHARACTERISTIC POLYNOMIALS OF RANDOM ELEMENTS IN ARITHMETIC GROUPS
SPLITTING FIELDS CHARACTERISTIC POLYNOMIALS RANDOM ELEMENTS ARITHMETIC GROUPS
2015/8/26
We discuss rather systematically the principle, implicit in earlier works, that for a “random” element in an arithmetic subgroup of a (split, say) reductive algebraic group over a number field, the sp...
Henon Mappings in the Complex Domain II:projective and inductive limits of polynomials
Henon Mappings Complex Domain projective and inductive limits
2015/8/26
Henon Mappings in the Complex Domain II:projective and inductive limits of polynomials.
How to find all roots of complex polynomials by Newton’s method
complex polynomials Newton’s method
2015/8/26
We investigate Newton’s method to find roots of polynomials of fixed degree d, appropriately normalized: we construct a finite set of points such that, for every root of every such polynomial, at leas...
Factorization of the Cyclotomic Polynomials Q2^(n+1)(x)
Algebra cyclotomic polynomial order of an integer Factorization theorem
2011/9/25
In this paper we study the factorization of the polynomials 1+x^(2^n)over a field K, which have the same form as the Fermat numbers . As we notice that 1+x^(2^n) is equal to the 2^(n+1)th cyclotomic p...
Factorization of the Cyclotomic Polynomials Qp^(n+1)(x)
Algebra cyclotomic polynomial order of an integer Factorization theorem
2011/9/25
In this paper we study the factorization of the p^(n+1)th cyclotomic polynomials Qp^(n+1)(x) over a field K for prime p>2 and integer n>=0. Our methodology to solve the problem is due to some conclusi...
Canonical Factorization of cyclotomic polynomials
algebra finite fields order of an integer cyclotomic polynomials factorization
2011/9/25
In this article, we studied the order of an integer q modulo integer m, and then studied the factorization of the mth cyclotomic polynomial over a field K. We discussed the order of q modulo m by the ...
Cyclotomic Polynomials and Factorization Theorems
algebra finite fields order of an integer cyclotomic polynomials factorization theorem
2011/9/24
Let Qm(x) be the mth cyclotomic polynomial over finite field Fq. The factorization of Qm(x^t) and f(x^t) over Fq are discussed, where t is an positive integer larger than one and f(x) is any irreducib...
Decomposition of Polynomials
Decomposition of Polynomials Commutative Algebra Symbolic Computation
2011/8/25
Abstract: This diploma thesis is concerned with functional decomposition $f = g \circ h$ of polynomials. First an algorithm is described which computes decompositions in polynomial time. This algorith...
Recurrence Relations for Strongly q-Log-Convex Polynomials
log-concave q-log-convexity strong q-log-convexity Bell polynomials Bessel polynomials Ramanujan polynomials Dowling polynomials
2014/6/3
We consider a class of strongly q-log-convex polynomials based on a triangular recurrence relation with linear coefficients, and we show that the Bell polynomials, the Bessel polynomials, the Ramanuja...
Chromatic polynomials of complementary (n,k)-clique pairs
Chromatic polynomials complementary (n,k)-clique pairs
2011/2/22
We introduce a class of pairs of graphs consisting of two cliques joined by an arbitrary number of edges. The members of a pair have the property that the clique-bridging edge-set of one graph is the ...