A bijective proof of Garsia's -Lagrange inversion theorem.
A Combinatorial Proof of the Existence of the Generic Hecke Algebra and R-Polynomials.
A common recursion for Laplacians of matroids and shifted simplicial complexes.
A generalization of combinatorial Nullstellensatz.
A simple method for estimating the bounds of spectral radius of nonnegative irreducible matrices.
Algebraically solvable problems: describing polynomials as equivalent to explicit solutions.
An algebraic theory of order
In this paper, we present an abstract framework which describes algebraically the derivation of order conditions independently of the nature of differential equations considered or the type of integrators used to solve them. Our structure includes a Hopf algebra of functions, whose properties are used to answer several questions of prime interest in numerical analysis. In particular, we show that, under some mild assumptions, there exist integrators of arbitrarily high orders for arbitrary (modified)...
Automorphisms and enumeration of switching classes of tournaments.