On sums over partially ordered sets.
On the asymptotic behavior of some counting functions
The investigation of certain counting functions of elements with given factorization properties in the ring of integers of an algebraic number field gives rise to combinatorial problems in the class group. In this paper a constant arising from the investigation of the number of algebraic integers with factorizations of at most k different lengths is investigated. It is shown that this constant is positive if k is greater than 1 and that it is also positive if k equals 1 and the class group satisfies...
On the behavior of a variant of Hofstadter's -sequence.
On the central coefficients of Bell matrices.
On the construction of non-isomorphic Steiner quadruple systems
On the density of languages representing finite set partitions.
On the diagram of Schröder permutations.
On the distribution of the -Euler polynomials and the -Genocchi polynomials of higher order.
On the dominance partial ordering of Dyck paths.
On the doubly refined enumeration of alternating sign matrices and totally symmetric self-complementary plane partitions.
On the entropy and letter frequencies of ternary square-free words.
On the enumeration of a class of plane multigraphs.
On the equivalence of addition formula of lattice paths and the Kolmogorov equation of birth and death processes.
On the Eulerian enumeration of involutions.
On the generation and enumeration of some classes of convex polyominoes.
On the genus distribution of -dipoles.
On the Horton-Strahler number for combinatorial tries
On the Horton-Strahler Number for Combinatorial Tries
In this paper we investigate the average Horton-Strahler number of all possible tree-structures of binary tries. For that purpose we consider a generalization of extended binary trees where leaves are distinguished in order to represent the location of keys within a corresponding trie. Assuming a uniform distribution for those trees we prove that the expected Horton-Strahler number of a tree with α internal nodes and β leaves that correspond to a key is asymptotically given by provided that α...
On the non-holonomic character of logarithms, powers, and the th prime function.
On the number of derangements of a sharply k-ply transitive set of permutations.