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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. ...
Representations of quivers with automorphisms over finite fields
quiver with automorphism hereditary algebra representation
2011/9/28
Let ${mathbb F}_q$ be the finite field of $q$ elements and $k$ be its algebraic closure. Let $Q$ be a quiver with automorphism $sigma$. In this survey we focus on the study of modules over the ${mathb...
Randomized Communication Complexity for Linear Algebra Problems over Finite Fields
communication complexity streaming, matrix singularity determinant
2012/12/3
Finding the singularity of a matrix is a basic problem in linear algebra. Chu and Schnitger first considered this problem in the communication complexity model, in which Alice holds the first half of ...
On explicit factors of Cyclotomic polynomials over finite fields
Cyclotomic polynomials finite fields
2010/11/24
We study the explicit factorization of $2^n r$-th cyclotomic polynomials over finite field $\mathbb{F}_q$ where $q, r$ are odd with $(r, q) =1$. We show that all irreducible factors of $2^n r$-th cyc...
Relatively Prime Polynomials and Nonsingular Hankel Matrices over Finite Fields
Relatively Prime Polynomials Nonsingular Hankel Matrices
2010/11/12
The probability for two monic polynomials of a positive degree n with coefficients in the finite field F_q to be relatively prime turns out to be identical with the probability for an n x n Hankel ma...
Restriction estimates for the paraboloid over finite fields
Restriction estimates paraboloid over finite fields
2010/12/7
We prove certain endpoint restriction estimates for the paraboloid over finite fields in
three and higher dimensions. Working in the bilinear setting, we are able to pass from esti-
mates for charac...
Explicit incidence bounds over general finite fields
Explicit incidence bounds general finite fields
2010/12/9
Let Fq be a finite field of order q = pk where p is prime. Let P and L be sets of points and lines respectively in Fq×Fq with |P| = |L| = n. We establish the incidence bound I(P,L)
n 3 2 − 1...
Minimal Achievable Approximation Ratio for MAX-MQ in Finite Fields
Multivariate quadratic polynomial equations MAX-MQ approximation algorithm approximation ratio
2013/9/9
Given a multivariate quadratic polynomial system in a niteeld Fq, theproblem MAX-MQ is to ˉnd a solution satisfying the maximal number of equations. We prove that the probability of a random assignmen...