### A bijective proof of Garsia's $q$-Lagrange inversion theorem.

Skip to main content (access key 's'),
Skip to navigation (access key 'n'),
Accessibility information (access key '0')

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)...

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...

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.

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...