Elementary proofs and the sums differences problem.
In this paper, we rule out the possibility that a certain method of proof in the sums differences conjecture can settle the Kakeya Conjecture.
Elementary proofs for convolution identities of Abel and Hagen-Rothe.
Elementary -identities. (Elementare -Identitäten.)
Elevation of a graph
Elimination of local bridges
Elliptic semiplanes and group divisible designs with orthogonal resolutions.
e-locally acyclic graphs
Elongation in a graph
Embedding -homogeneous latin trades into abelian -groups
Let be a partial latin square and be a latin square with . We say that is a latin trade if there exists a partial latin square with such that is a latin square. A -homogeneous latin trade is one which intersects each row, each column and each entry either or times. In this paper, we show the existence of -homogeneous latin trades in abelian -groups.
Embedding a forest in a graph.
Embedding arbitrary graphs into strongly regular and distance-regular graphs.
Embedding complete ternary trees into hypercubes
We inductively describe an embedding of a complete ternary tree Tₕ of height h into a hypercube Q of dimension at most ⎡(1.6)h⎤+1 with load 1, dilation 2, node congestion 2 and edge congestion 2. This is an improvement over the known embedding of Tₕ into Q. And it is very close to a conjectured embedding of Havel [3] which states that there exists an embedding of Tₕ into its optimal hypercube with load 1 and dilation 2. The optimal hypercube has dimension ⎡(log₂3)h⎤ ( = ⎡(1.585)h⎤) or ⎡(log₂3)h⎤+1....
Embedding graphs in their complements
Embedding infinite trees into a cube of infinite dimension
Embedding -quasistars into -cubes
Embedding properties of endomorphism semigroups
Denote by PSelf Ω (resp., Self Ω) the partial (resp., full) transformation monoid over a set Ω, and by Sub V (resp., End V) the collection of all subspaces (resp., endomorphisms) of a vector space V. We prove various results that imply the following: (1) If card Ω ≥ 2, then Self Ω has a semigroup embedding into the dual of Self Γ iff . In particular, if Ω has at least two elements, then there exists no semigroup embedding from Self Ω into the dual of PSelf Ω. (2) If V is infinite-dimensional, then...
Embedding the polytomic tree into the -cube
Embedding trees into block graphs
Embedding trees into clique-bridge-clique graphs
Embedding vertices at points: Few bends suffice for planar graphs.