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

collaborators

12 papers

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…

math.CO2025

Cayley graphs on elementary abelian groups of extreme degree have complete cores

Guang Rao, Colin Tan

Nešetřil and Šámal asked whether every cubelike graph has a cubelike core. Mančinska, Pivotto, Roberson and Royle answered this question in the affirmative for cubelike graphs whos…

math.PR2022

Probability bounds for $n$ random events under $(n - 1)$ -wise independence

Karthik Natarajan, Arjun Kodagehalli Ramachandra, Colin Tan

A collection of $n$ random events is said to be $(n - 1)$ -wise independent if any $n - 1$ events among them are mutually independent. We characterise all probability measures with…

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.CV2017★ 1 cited

Characterization of polynomials whose large powers have all positive coefficients

Colin Tan, Wing-Keung To

We give a criterion which characterizes a homogeneous real multi-variate polynomial to have the property that all sufficiently large powers of the polynomial (as well as their prod…

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…

math.DG2016

Eventual positivity of Hermitian algebraic functions and associated integral operators

Colin Tan, Wing-Keung To

Quillen proved that repeated multiplication of the standard sesquilinear form to a positive Hermitian bihomogeneous polynomial eventually results in a sum of Hermitian squares, whi…

math.AT2015

Loop homological invariants associated to real projective spaces

Man Gao, Colin Tan, Jie Wu

Let A be a based subspace of Y. Under the assumptions that Y is path-connected and that the reduced diagonal map of A induces the zero map in all mod 2 reduced homology groups, we…

math.DG2014

Eventual positivity of Hermitian polynomials and integral operators

Colin Tan

Quillen proved that, if a Hermitian bihomogeneous polynomial is strictly positive on the unit sphere, then repeated multiplication of the standard sesquilinear form to this polynom…

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

Cayley graphs on elementary abelian groups of extreme degree have complete cores

Probability bounds for n random events under (n−1)-wise independence

Improved effective estimates of Pólya's Theorem for quadratic forms

Archimedean Representation Theorem for modules over a commutative ring

Characterization of polynomials whose large powers have all positive coefficients

A Positivstellensatz for forms on the positive orthant

Eventual positivity of Hermitian algebraic functions and associated integral operators

Loop homological invariants associated to real projective spaces

Eventual positivity of Hermitian polynomials and integral operators

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

Probability bounds for $n$ random events under $(n - 1)$ -wise independence