Updated information on "Positivity problems and conjectures in algebraic combinatorics"

• A solution to Problem 2 for convex polytopes was given by Kalle Karu, with a strengthening by Paul Bressler and Valery A. Lunts.
  
  
• Some progress on Problem 4 is due to Victor Reiner and his colloborators Naichung Conan Leung, Dennis Stanton, and Volkmar Welker. The paper with Welker is also related to Problem 20.
  
  
• The conjecture following Problem 9 is false as stated. Pavlo Pylyavskyy pointed out that if \lambda ≥ \lambda' then it may not be the case that |\Pi_\lambda| ≤ |\Pi_{\lambda'}|, the smallest example being \lambda = (6,2,2,1,1) and \lambda' = (5,3,1,1,1,1). The conjecture remains open if modified to state that \phi_\lambda has full rank when \lambda ≥ \lambda', though this may very well be false. The original conjecture remains open in the case that would imply the Foulkes plethysm conjecture, viz., \lambda has m parts equal to n, where n ≥ m. However, a counterexample in that case was announced by J. Müller and Max Neunhoeffer, but details have not yet appeared.
  
  
• A solution to the conjecture of Sundaram mentioned shortly after Problem 9 was found by Ben Joseph in April, 2000.
  
  
• A solution to Problem 13 (the nonnegativity of the coefficients of the (q,t)-Kostka polynomials) has been given by Mark Haiman.
  
  
• Problem 23 was