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Reports tagged with Arithmetic formula:
TR22-042 | 31st March 2022
Vikraman Arvind, Pushkar Joglekar

#### Matrix Polynomial Factorization via Higman Linearization

In continuation to our recent work on noncommutative
polynomial factorization, we consider the factorization problem for
matrices of polynomials and show the following results.
\begin{itemize}
\item Given as input a full rank $d\times d$ matrix $M$ whose entries
$M_{ij}$ are polynomials in the free noncommutative ring
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TR22-157 | 16th November 2022
Pranjal Dutta, Fulvio Gesmundo, Christian Ikenmeyer, Gorav Jindal, Vladimir Lysikov

#### Border complexity via elementary symmetric polynomials

In (ToCT’20) Kumar surprisingly proved that every polynomial can be approximated as a sum of a constant and a product of linear polynomials. In this work, we prove the converse of Kumar's result which ramifies in a surprising new formulation of Waring rank and border Waring rank. From this conclusion, ... more >>>

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