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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. ...
Hyperbolicity cones of elementary symmetric polynomials are spectrahedral
hyperbolic polynomials hyperbolicity cones spectrahedral cones elementary symmetric polynomials spanning trees matrix-tree theorem
2012/4/16
We prove that the hyperbolicity cones of elementary symmetric polynomials are spectrahedral, i.e., they are slices of the cone of positive semidefinite matrices. The proof uses the matrix--tree theore...
Relative symmetric polynomials and money change problem
Money change problem Partitions of integers
2011/1/21
This article is devoted to the number of non-negative solu-tions of the linear Diophantine equation a1t1 + a2t2 + · · · antn = d,
The Convolution Ring of Arithmetic Functions and Symmetric Polynomials
Arithmetic functions Multiplicative functions Additive functions
2010/12/3
Inspired by Rearick (1968), we introduce two new operators, LOG and EXP.The LOG operates on generalized Fibonacci polynomials giving generalized Lucas polynomials.The EXP is the inverse of LOG.
Inequalities Related to Rearrangements of Powers and Symmetric Polynomials
Symmetric Polynomials Permutations Inequalities
2008/7/1
Inequalities Related to Rearrangements of Powers and Symmetric Polynomials.
New Inequalities Between Elementary Symmetric Polynomials
Elementary Symmetric Polynomials New Inequalities
2008/6/30
New families of sharp inequalities between elementary symmetric polynomials are proven. We estimate above and below by the elementary symmetric polynomials in the case, when are non-negative real n...