Independence of hyperlogarithms over function fields via algebraic   combinatorics
  We obtain a necessary and sufficient condition for the linear independence of solutions of differential equations for hyperlogarithms. The key fact is that the multiplier (i.e. the factor $M$ in the differential equation $dS=MS$) has only singularities of first order (Fuchsian-type equations) and this implies that they freely span a space which contains no primitive. We give direct applications where we extend the property of linear independence to the largest known ring of coefficients. 
Matthieu Deneufch\^atel (LIPN), G\'erard Henry Edmond Duchamp (LIPN),   Vincel Hoang Ngoc Minh (LIPN), Allan I. Solomon (LPTMC)
math.CO cs.SC