We investigate the asymptotic number of elements of size n in a particular class of closed lambda-terms (so-called BCI(p)-terms) which are generalizations of lambdaterms related to axiom systems of combinatory logic. By deriving a differential equation for the generating function of the counting sequence we obtain a recurrence relation which can be solved asymptotically. We derive differential ...

Motivated by the recent proof of the Stanley-Wilf conjecture, we study the asymptotic behavior of the number of permutations avoiding a generalized pattern. Generalized patterns allow the requirement that some pairs of letters must be adjacent in an occurrence of the pattern in the permutation, and consecutive patterns are a particular case of them. We determine the asymptotic behavior of the n...

Counting the number of elements in finite sets Si (where i typically ranges over some index set I such as the non–negative integers or a cartesian product of the non–negative integers) is surely one of the oldest and most fundamental problems in mathematics. It is in the nature of the subject that only a few enumeration problems have a compact solution in terms of a simple explicit formula in i...

Let x = (x1, x2, . . . , xn) ∈ Nn . Define a x-parking function to be a sequence (a1, a2, . . . , an) of positive integers whose non-decreasing rearrangement b1 ≤ b2 ≤ · · · ≤ bn satisfies bi ≤ x1+ · · ·+xi. Let Pn(x) denote the number of x-parking functions. We discuss the enumerations of such generalized parking functions. In particular, We give the explicit formulas and present two proofs, o...

Implicit-function theorems for generalized equations play an important role in many applications, especially in the stability and sensitivity analysis of variational inequalities and optimization problems and in the convergence analysis of numerical algorithms solving such problems. We refer for instance to Fiacco [7] and Ioffe and Tihomirov [9] for applications of the classical implicit-functi...

In the present paper we elaborate on the underlying Hamiltonian structure of interconnected energy-conserving physical systems. It is shown that a power-conserving interconnection of port-controlled generalized Hamiltonian systems leads to an implicit generalized Hamiltonian system, and a power-conserving partial interconnection to an implicit port-controlled Hamil-tonian system. The crucial co...

In this paper, we introduce the new class of implicit L-stable generalized hybrid methods for the numerical solution of first order initial value problems. We generalize the hybrid methods with utilize ynv directly in the right hand side of classical hybrid methods. The numerical experimentation showed that our method is considerably more efficient compared to well known methods used for the n...

The automata-theoretic approach for the verification of linear time properties involves checking the emptiness of a Büchi automaton. However generalized Büchi automata, with multiple acceptance sets, are preferred when verifying under weak fairness hypotheses. Existing emptiness checks for which the complexity is independent of the number of acceptance sets are all based on the enumeration of S...