3 papers
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- 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
NeÅ¡etÅil and Šámal asked whether every cubelike graph has a cubelike core. ManÄinska, Pivotto, Roberson and Royle answered this question in the affirmative for cubelike graphs…
math.AG2024
Improved effective estimates of Pólya's Theorem for quadratic forms
Colin Tan
Following de Loera and Santos, the Pólya exponent of a -ary real form (i.e. a homogeneous polynomial in variables with real coefficients) is the infimum of the upward c…