Über (k + 1)-kritisch (2k + 1)-fach zusammenhängende Graphen

A Combinatorial Proof of a Relationship Between Maximal $(2k-1, 2k+1)$-Cores and $(2k-1, 2k, 2k+1)$-Cores

Integer partitions which are simultaneously t–cores for distinct values of t have attracted significant interest in recent years. When s and t are relatively prime, Olsson and Stanton have determined the size of the maximal (s, t)-core κs,t. When k > 2, a conjecture of Amdeberhan on the maximal (2k − 1, 2k, 2k + 1)-core κ2k−1,2k,2k+1 has also recently been verified by numerous authors. In this ...

Über ein Fach ohne Namen und Struktur

Die Wissenschaft ist in Fächer (oder Disziplinen) unterteilt, die sich über die Jahrhunderte etabliert haben. Beispielsweise ist die Physik ein solches Fach und zwar ein sehr großes Fach, das unter seinem Dach viele sehr unterschiedliche Fachgebiete vereint. Gleichwohl gibt es innerhalb der Physik Einigkeit über die innere Zusammengehörigkeit über diese Vielfalt hinweg. Diese Einigkeit beruht a...

On the coexistence of conference matrices and near resolvable 2-(2k+1, k, k-1) designs

We show that a near resolvable 2-(2k + 1, k, k − 1) design exists if and only if a conference matrix of order 2k+2 does. A known result on conference matrices then allows us to conclude that a near resolvable 2-(2k + 1, k, k − 1) design with even k can only exist if 2k + 1 is the sum of two squares. In particular, neither a near resolvable 2-(21, 10, 9) design nor a near resolvable 2-(33, 16, 1...

Optimal Consecutive-k-out-of-(2k+1): G Cycle

We present a complete proof for the invariant optimal assignment for consecutive-k-outof-(2k+1):G cycle, which was proposed by Zuo and Kao in 1990 with an incomplete proof, pointed out recently by Jalali, Hawkes, Cui and Hwang.

Multiplier with Parallel CSA Using CRT's Specific Moduli (2k-1, 2k , 2k+1)