Positivity problems in enumerative and algebraic combinatorics

This website is launching on the occasion of the conference “Interactions between Combinatorics, Analysis and Statistical Physics” (22–24 June 2026, University College London), held in (belated) celebration of Alan Sokal's 70th birthday.

It will serve as a repository of the many conjectures that Alan has been posing, with a particular focus on enumerative and algebraic combinatorics. This repository will be actively maintained and updated with new conjectures as they arise. Even though the list is maintained by his students and colleagues, currently, this website is maintained by Bishal Deb.


While the majority of the problems collected here are due to Alan Sokal, the list also includes several conjectures posed by other researchers — particularly those that are closely related to Alan's interests or that have emerged from discussions at conferences and seminars over the years. Each problem is clearly attributed to its originator.

Themes

The problems shared on this website can be broadly organised into the following themes.

T1. Stieltjes moment sequences and coefficientwise hankel total positivity

  1. T1.7. Permutation patterns and Stieltjes moment sequences, coefficientwise Hankel total positivity
  2. T1.8. Maps and Stieltjes moment sequences, coefficientwise Hankel total positivity

T2. Total positivity of combinatorial matrices

T3. Symmetric functions and total positivity

T4. Distribution of zeroes in the complex plane

T5. Miscellaneous

📩 Contribute to a problem? Found a partial result, a counterexample, or a new reference?