A problem on matrices
A product theorem for Skolem sequences.
A prolific construction of strongly regular graphs with the -e. c. property.
A proof of a conjecture of Knuth.
A proof of menger's theorem by contraction
A short proof of the classical theorem of Menger concerning the number of disjoint AB-paths of a finite graph for two subsets A and B of its vertex set is given. The main idea of the proof is to contract an edge of the graph.
A proof of some Schützenberger-type results for Eulerian paths and circuits on digraphs.
A proof of the bounded graph conjecture.
A proof of the crossing number of in a surface
In this note we give a simple proof of a result of Richter and Siran by basic counting method, which says that the crossing number of in a surface with Euler genus ε is ⎣n/(2ε+2)⎦ n - (ε+1)(1+⎣n/(2ε+2)⎦).
A proof of the identities of Gordon and MacMahon and two new identities. (La démonstration des identités de Gordon et MacMahon et de deux identités nouvelles.)
A proof of the two-path conjecture.
A property of canonical graphs.
A property of eigenvectors of nonnegative symmetric matrices and its application to graph theory
A Property Of The Number Of Perfect Matchings Of A Graph
A -analogue of an inequality due to Konrad Knopp.
A -analogue of de Finetti's theorem.
A -analogue of Faulhaber's formula for sums of powers.
A -analogue of Graham, Hoffman and Hosoya's theorem.
A q-analogue of complete monotonicity
The aim of this paper is to give a q-analogue for complete monotonicity. We apply a classical characterization of Hausdorff moment sequences in terms of positive definiteness and complete monotonicity, adapted to the q-situation. The method due to Maserick and Szafraniec that does not need moments turns out to be useful. A definition of a q-moment sequence appears as a by-product.
A q-analogue of Lehmer's congruence
A quantitative aspect of non-unique factorizations: the Narkiewicz constants II
Let K be an algebraic number field with non-trivial class group G and be its ring of integers. For k ∈ ℕ and some real x ≥ 1, let denote the number of non-zero principal ideals with norm bounded by x such that a has at most k distinct factorizations into irreducible elements. It is well known that behaves, for x → ∞, asymptotically like . In this article, it is proved that for every prime p, , and it is also proved that if and m is large enough. In particular, it is shown that for...