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.GR2026

Detecting divisibility in uniquely divisible $N$ -semigroups via homomorphisms to $R_{> 0}$

Colin Tan

An $N$ -semigroup is an archimedean, idempotent-free, cancellative and commutative semigroup. For example, the additive semigroup $R_{> 0}$ of strictly positive r…

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…

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

Detecting divisibility in uniquely divisible N-semigroups via homomorphisms to R>0​

Positivity of polynomials on the nonnegative part of certain affine hypersurfaces

Detecting divisibility in uniquely divisible $N$ -semigroups via homomorphisms to $R_{> 0}$