A proof of the monotone column permanent (MCP) conjecture for dimension 4 via sums-of-squares of rational functions

Authors:
Erich Kaltofen;Zhengfeng Yang;Lihong Zhi
Affiliations:
North Carolina State University, Raleigh, NC, USA;East China Normal University, Shanghai, China;Academy of Mathematics and Systems Science, Beijing, China
Venue:
Proceedings of the 2009 conference on Symbolic numeric computation
Year:
2009

Citing 5
Cited 2

Further investigations involving rook polynomials with only real zeros

European Journal of Combinatorics
GloptiPoly: Global optimization over polynomials with Matlab and SeDuMi

ACM Transactions on Mathematical Software (TOMS)
A Macaulay 2 package for computing sum of squares decompositions of polynomials with rational coefficients

Proceedings of the 2007 international workshop on Symbolic-numeric computation
Computing the global optimum of a multivariate polynomial over the reals

Proceedings of the twenty-first international symposium on Symbolic and algebraic computation
Exact certification of global optimality of approximate factorizations via rationalizing sums-of-squares with floating point scalars

Proceedings of the twenty-first international symposium on Symbolic and algebraic computation

Deciding reachability of the infimum of a multivariate polynomial

Proceedings of the 36th international symposium on Symbolic and algebraic computation
Certificates of impossibility of Hilbert-Artin representations of a given degree for definite polynomials and functions

Proceedings of the 37th International Symposium on Symbolic and Algebraic Computation

Quantified Score

Hi-index	0.00

Visualization

Abstract

For a proof of the monotone column permanent (MCP)conjecture for dimension 4 it is sufficient to show that 4 polynomials, which come from the permanents of real matrices, are nonnegative for all real values of the variables, where the degrees and the number of the variables of these polynomials are all 8. Here we apply a hybrid symbolic-numerical algorithm for certifying that these polynomials can be written as an exact fraction of two polynomial sums-of-squares (SOS) with rational coefficients.