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- W2952617164 abstract "We introduce and study the notion of read-$k$ projections of the determinant: a polynomial $f in mathbb{F}[x_1, ldots, x_n]$ is called a {it read-$k$ projection of determinant} if $f=det(M)$, where entries of matrix $M$ are either field elements or variables such that each variable appears at most $k$ times in $M$. A monomial set $S$ is said to be expressible as read-$k$ projection of determinant if there is a read-$k$ projection of determinant $f$ such that the monomial set of $f$ is equal to $S$. We obtain basic results relating read-$k$ determinantal projections to the well-studied notion of determinantal complexity. We show that for sufficiently large $n$, the $n times n$ permanent polynomial $Perm_n$ and the elementary symmetric polynomials of degree $d$ on $n$ variables $S_n^d$ for $2 leq d leq n-2$ are not expressible as read-once projection of determinant, whereas $mon(Perm_n)$ and $mon(S_n^d)$ are expressible as read-once projections of determinant. We also give examples of monomial sets which are not expressible as read-once projections of determinant." @default.
- W2952617164 created "2019-06-27" @default.
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- W2952617164 date "2015-08-26" @default.
- W2952617164 modified "2023-10-04" @default.
- W2952617164 title "On the expressive power of read-once determinants" @default.
- W2952617164 cites W1979337672 @default.
- W2952617164 doi "https://doi.org/10.48550/arxiv.1508.06511" @default.
- W2952617164 hasPublicationYear "2015" @default.
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