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.
Chain polynomials of distributive lattices are 75% unimodal.
Combinatoria e Topologia. Alcune considerazioni generali
Si descrive un metodo generale mediante il quale associare in modo naturale spazi topologici ad insiemi parzialmente ordinati e funzioni continue afunzioni monotone tra di essi; questa associazione è chiaramente la chiave di volta per fondare l’utilizzo di metodi topologici nella teoria combinatoria degli insiemi parzialmente ordinati. Si discutono quindi alcuni criteri di contraibilità e si presenta una breve introduzione alla teoria dei «poset Cohen-Macaulay». Il lavoro si conclude con una sezione...
Combinatorial aspects of polylogarithms and Euler-Zagier sums. (Aspects combinatoires des polylogarithmes et des sommes d'Euler-Zagier.)
Combinatorial interpretations for rank-two cluster algebras of affine type.
Connectivity, toughness, spanning trees of bounded degree, and the spectrum of regular graphs
The eigenvalues of graphs are related to many of its combinatorial properties. In his fundamental work, Fiedler showed the close connections between the Laplacian eigenvalues and eigenvectors of a graph and its vertex-connectivity and edge-connectivity. We present some new results describing the connections between the spectrum of a regular graph and other combinatorial parameters such as its generalized connectivity, toughness, and the existence of spanning trees with bounded degree.
Cospectral graphs on 12 vertices.
Criteria for shellable multicomplexes.
Forestation in hypergraphs: Linear -trees.
Graphical condensation, overlapping Pfaffians and superpositions of matchings.
-vectors, Eulerian polynomials and stable polytopes of graphs.
Inverse zero-sum problems in finite Abelian p-groups
We study the minimal number of elements of maximal order occurring in a zero-sumfree sequence over a finite Abelian p-group. For this purpose, and in the general context of finite Abelian groups, we introduce a new number, for which lower and upper bounds are proved in the case of finite Abelian p-groups. Among other consequences, our method implies that, if we denote by exp(G) the exponent of the finite Abelian p-group G considered, every zero-sumfree sequence S with maximal possible length over...
New Euler-Mahonian permutation statistics.