Planar coincidence site lattices and modules with N -fold symmetry are well understood in a formulation based on cyclotomic fields, in particular for the class number one case, where they appear as certain principal ideals in the corresponding ring of integers. We extend this approach to multiple coincidences, which apply to triple or multiple junctions. In particular, we give explicit results ...

n-Fold integer programming is a fundamental problem with a variety of natural applications in operations research and statistics. Moreover, it is universal and provides a new, variable-dimension, parametrization of all of integer programming. The fastest algorithm for n-fold integer programming predating the present article runs in time O ( ng(A)L ) with L the binary length of the numerical par...

Recently, the study of patterns in inversion sequences was initiated by Corteel–Martinez–Savage–Weselcouch and Mansour–Shattuck independently. Motivated their works a double Eulerian equidistribution due to Foata (1977), we investigate several classical statistics on restricted that are either known or conjectured be enumerated Catalan, Large Schröder, Baxter Euler numbers. One two highlights o...

Integer Linear Programming is a famous NP-complete problem. Lenstra showed that in the case of small dimension, it can be solved in polynomial time. This algorithm became a ubiquitous tool, especially in the design of parameterized algorithms for NP-complete problems, where we wish to isolate the hardness of an instance to some parameter. However, it was discovered that in many cases using Lens...

Scheduling problems are fundamental in combinatorial optimization. Much work has been done on approximation algorithms for NP-hard cases, but relatively little is known about exact solutions when some part of the input is a fixed parameter. In 2014, Mnich and Wiese initiated a systematic study in this direction. In this paper we continue this study and show that several additional cases of fund...

MOTIVATION Homology search for RNAs can use secondary structure information to increase power by modeling base pairs, as in covariance models, but the resulting computational costs are high. Typical acceleration strategies rely on at least one filtering stage using sequence-only search. RESULTS Here we present the multi-segment CYK (MSCYK) filter, which implements a heuristic of ungapped stru...

Two cases of obstinate cancers are cured by a new hypothesis synergistic therapy approach where Cancer Homoeotherapeutics were analysed scientifically immunotherapy modus operandi homoeopathic medicine selection is done activating natural cancer immunity killer cells (NK) through the interferon produced viral infection. So synthesis antiviral and antimiasmatic to treat cases.