Add to ORKGIn this paper, we study the complex simultaneous Waring rank for collections of monomials. For general collections, we provide a lower bound, whereas for special collections we provide a formula for the simultaneous Waring rank. Our approach is algebraic and combinatorial. We give an application to ranks of binomials and maximal simultaneous ranks. Moreover, we include an appendix of scripts written in the algebra software Macaulay2 to experiment with simultaneous ranks. © 2018 University of Illinois
A Waring decomposition of a polynomial is an expression of the polynomial as a sum of powers of line...
Algebraic models of phenomena arising from different fields utilize the polynomial ring P in a finit...
This thesis is about monomial orderings and a division algorithm for polynomials in two or more vari...
In this paper we compute the Waring rank of any polynomial of the form , F=M1+...+Mr, where the Mi a...
In this paper we compute the Waring rank of any polynomial of the form F=M1+...+Mr, where the Mi a...
AbstractIn this paper we compute the Waring rank of any polynomial of the form F=∑i=1rMi, where the ...
AbstractIn this paper we compute the Waring rank of any polynomial of the form F=∑i=1rMi, where the ...
We show that monomials and sums of pairwise coprime monomials in four or more variables have Waring ...
Motivated by recent results on the Waring problem for polynomial rings and representation of monomia...
Motivated by recent results on the Waring problem for polynomial rings and representation of monomia...
Motivated by recent results on the Waring problem for polynomial rings [4] and representation of mon...
Motivated by recent results on the Waring problem for polynomial rings [4] and representation of mon...
We shall give simpler proofs of some lower bounds on monotone computations. We describe a simple con...
Abstract We define some variations of the Scott rank for countable models and obtain some inequaliti...
Among all the restrictions of weight orders to the subsets of monomials with a fixed degree, we cons...
A Waring decomposition of a polynomial is an expression of the polynomial as a sum of powers of line...
Algebraic models of phenomena arising from different fields utilize the polynomial ring P in a finit...
This thesis is about monomial orderings and a division algorithm for polynomials in two or more vari...
In this paper we compute the Waring rank of any polynomial of the form , F=M1+...+Mr, where the Mi a...
In this paper we compute the Waring rank of any polynomial of the form F=M1+...+Mr, where the Mi a...
AbstractIn this paper we compute the Waring rank of any polynomial of the form F=∑i=1rMi, where the ...
AbstractIn this paper we compute the Waring rank of any polynomial of the form F=∑i=1rMi, where the ...
We show that monomials and sums of pairwise coprime monomials in four or more variables have Waring ...
Motivated by recent results on the Waring problem for polynomial rings and representation of monomia...
Motivated by recent results on the Waring problem for polynomial rings and representation of monomia...
Motivated by recent results on the Waring problem for polynomial rings [4] and representation of mon...
Motivated by recent results on the Waring problem for polynomial rings [4] and representation of mon...
We shall give simpler proofs of some lower bounds on monotone computations. We describe a simple con...
Abstract We define some variations of the Scott rank for countable models and obtain some inequaliti...
Among all the restrictions of weight orders to the subsets of monomials with a fixed degree, we cons...
A Waring decomposition of a polynomial is an expression of the polynomial as a sum of powers of line...
Algebraic models of phenomena arising from different fields utilize the polynomial ring P in a finit...
This thesis is about monomial orderings and a division algorithm for polynomials in two or more vari...