Finding Patterns Avoiding Many Monochromatic Constellations

Enumeration Schemes for Words Avoiding Permutations

The enumeration of permutation classes has been accomplished with a variety of techniques. One wide-reaching method is that of enumeration schemes, introduced by Zeilberger and extended by Vatter. In this paper we further extend the method of enumeration schemes to words avoiding permutation patterns. The process of finding enumeration schemes is programmable and allows for the automatic enumer...

Re-clustering of Constellations through Machine Learning

Since thousands of years ago, people around the world have been looking up into the sky, trying to find patterns of visible stars’ distribution, and dividing them into different groups called constellations. Originally, constellations are recognized and organized by people’s imaginations based on the shapes of the star distribution. The most two famous groups of stars is the “Big Dipper” and th...

Coloring Graphs Using Two Colors While Avoiding Monochromatic Cycles

Avoiding Monochromatic Cycles Fabrice Talla Nobibon HEC-Management School, University of Liège, Rue Louvrex 14, Building N1, B-4000 Liège, Belgium, [email protected] Cor A.J. Hurkens Eindhoven University of Technology, Department of Mathematics and Computer Science. P.O. Box 513, 5600 MB Eindhoven, the Netherlands, [email protected] Roel Leus, Frits C.R. Spieksma University of Leuve...

Edge-colorings of graphs avoiding fixed monochromatic subgraphs with linear Turán number

تحلیل ساختار هندسی واگیره ماهی درهم در فرش هراتی

motifs in Iranian carpets is the best-known “Herati” design, also known as “Mahi-dar-ham”, which has been the focus of attention in most weaving centers in decorating carpet fields. The sub-patterns of this design have been slightly modified to add variety to this design. Despite many intricate Islimi (Arabesque) and Khataiee (Tendrils) motis, Mahi-dar-ham is a simple vagire that covers the ove...