A generalized prism, or more specifically an (0, j)-prism of order 2n (where n is even) is a cubic graph consisting of two cycles u The question of factorization of complete bipartite graphs into (0, j)-prisms was completely settled by the author and S. Cichacz. Some partial results have also been obtained by them and P. Kovar and S. Dib. We will present a decomposition for another class of (0,...

Andrews, Lewis and Lovejoy introduced the partition function PD(n) as number of partitions n with designated summands. In a recent work, Lin studied PDt(n) which counts tagged parts over all He proved that PDt(3n+2) is divisible by 3. this paper, we first introduce structure named overline summands, counted PDt(n). We then define generalized rank summands give combinatorial interpretation congr...

Coulomb and CSB effects in the three-nucleon system within the dressed bag model for 2N and 3N forces. Abstract. Coulomb and charge-symmetry breaking effects in the 3 He ground state within the dressed dibaryon model developed recently for 2N and 3N forces are examined in detail. Particular attention has been paid to the Coulomb displacement energy ∆E C = E B (3 H) − E B (3 He) and rms charge r...

Paul [ PJ first proved a 2.Sn-Iower bound for the network complex ity of an explicit boole an function. We mo dify the defi n ition of Pa ul's func tion a little a nd prove a 3n-I ower bound for th e network complexity of that function.-1

More than 50 years ago, the Cambridge undergraduate Bryan Birch showed that “3N points in a plane” can be split into N triples that span triangles with a non-empty intersection. He also conjectured a sharp, higher-dimensional version of this, which was proved by Helge Tverberg in 1964 (freezing, in a hotel room in Manchester). In a 1988 Computational Geometry paper, Bárány, Füredi & Lovász note...

In this paper, we show that any proof of the Collatz 3n + 1 Conjecture must have an infinite number of lines. Therefore, no formal proof is possible. We also discuss whether the proof strategy in this paper has any promise for proving that the Riemann Hypothesis is also unprovable.

We prove the following intersection and covering Helly-type theorems for boundaries of convex polygons in the plane. • Let S be a set of points in the plane. Let n¿ 4. If any 2n+2 points of S can be covered by the boundary of a convex n-gon, then S can be covered by the boundary of a convex n-gon. The value of 2n+ 2 is best possible in general. If n= 3, 2n+ 2 can be reduced to 7. • Let S be a 4...