Colin Tan

activity

20142026

most citedCharacterization of polynomials whose large powers have all positive coefficients

1 citations · 1 across the 10 of their papers we have counts for

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math.AG2026

A degree-linear upper bound for the Pólya exponent of forms with fixed arity

Yulong Li, Colin Tan

Let $P = \sum_{ω} a_{ω} x^{ω}$ be a degree $d$ homogeneous polynomial in $x_{0}, \dots, x_{n}$ with real coefficients. Pólya showed that, if $P$ is strictly positive on the standard $n$ -simpl…

math.AG2026

Positivity of polynomials on the nonnegative part of certain affine hypersurfaces

Colin Tan, Wing-Keung To

We consider polynomials on the intersection of the closed positive orthant with the height- $1$ level hypersurface of certain polynomials with positive coefficients. We show that an…

math.AG2018

Improved effective estimates of Pólya's Theorem for quadratic forms

Colin Tan

Following de Loera and Santos, the Pólya exponent of a $n$ -ary real form (i.e. a homogeneous polynomial in $n$ variables with real coefficients) $f$ is the infimum of the upward cl…

math.AG2017

Archimedean Representation Theorem for modules over a commutative ring

Colin Tan

Pólya's Positivstellensatz and Handelman's Positivstellensatz are known to be concrete instances of the abstract Archimedean Representation Theorem for (commutative unital) rings.…

math.AG2017

A Positivstellensatz for forms on the positive orthant

Claus Scheiderer, Colin Tan

Let $p$ be a nonconstant form in $R [x_{1}, \dots, x_{n}]$ with $p (1, \dots, 1) > 0$ . If $p^{m}$ has strictly positive coefficients for some integer $m \geq 1$ , we show that $p^{m}$ has str…