On a theorem of Landau. (Sur un théorème de Landau.)
On a Theorem of Livingstone and Wagner.
On a tiling scheme from M. C. Escher.
On a Two-Dimensional Search Problem
In this article we explore the so-called two-dimensional tree− search problem. We prove that for integers m of the form m = (2^(st) − 1)/(2^s − 1) the rectangles A(m, n) are all tight, no matter what n is. On the other hand, we prove that there exist infinitely many integers m for which there is an infinite number of n’s such that A(m, n) is loose. Furthermore, we determine the smallest loose rectangle as well as the smallest loose square (A(181, 181)). It is still undecided whether there exist...
On a two-sided Turán problem.
On a uniformly integrable family of polynomials defined on the unit interval.
On a unimodality conjecture in matroid theory.
On a variant of van der Waerden's theorem.
On acyclic colorings of direct products
A coloring of a graph G is an acyclic coloring if the union of any two color classes induces a forest. It is proved that the acyclic chromatic number of direct product of two trees T₁ and T₂ equals min{Δ(T₁) + 1, Δ(T₂) + 1}. We also prove that the acyclic chromatic number of direct product of two complete graphs Kₘ and Kₙ is mn-m-2, where m ≥ n ≥ 4. Several bounds for the acyclic chromatic number of direct products are given and in connection to this some questions are raised.
On acyclic hypergraphs of minimal prime models.
On Affinite Steiner Ternary Algebras
On algebras of generalized Latin squares
The main result of this paper is the introduction of a notion of a generalized -Latin square, which includes as a special case the standard Latin square, as well as the magic square, and also the double stochastic matrix. Further, the algebra of all generalized Latin squares over a commutative ring with identity is investigated. Moreover, some remarkable examples are added.
On Alperin's fusion theorem.
On alternating products of graph relations.
On amalgamation of graphs and essential sets of generators
On amply regular graphs with .
On an algorithm for a double-resolvability test.
On an algorithm to decide whether a free group is a free factor of another
We revisit the problem of deciding whether a finitely generated subgroup is a free factor of a given free group . Known algorithms solve this problem in time polynomial in the sum of the lengths of the generators of and exponential in the rank of . We show that the latter dependency can be made exponential in the rank difference rank - rank, which often makes a significant change.
On an algorithm to decide whether a free group is a free factor of another
We revisit the problem of deciding whether a finitely generated subgroup H is a free factor of a given free group F. Known algorithms solve this problem in time polynomial in the sum of the lengths of the generators of H and exponential in the rank of F. We show that the latter dependency can be made exponential in the rank difference rank(F) - rank(H), which often makes a significant change.
On an evaluation function for heuristic search as a path problem