Let A be a. matrix of m rows and n columns and let the entries of A be the integers 0 and 1. We call such a matrix a (0, 1) -matrix of size m by n. The 2 (0, 1)-matrices of size m by n play a fundamental role in a wide variety of combinatorial investigations. One of the chief reasons for this is the following. Let X be a set of n elements Xi, X2, • • • , xn and let Xi, X2, • • • , Xm be m subse...

In the last two decades institutional economics of development has been enriched by historical and, more recently, quantitative analysis of the effects of the quality of institutions on the pace and pattern of economic development. Following the leadership of Douglass North, this literature has shown how important secure property rights are in encouraging investment and innovations, allowing fo...

An extension of an induced path P in a graph G is ′ such that deleting the endpoints results P. said to be avoidable if each its extensions contained cycle. In 2019, Beisegel, Chudovsky, Gurvich, Milanič, and Servatius conjectured every contains k-vertex also same length, proved result for k = 2. The case 1 was known much earlier, due work Ohtsuki, Cheung, Fujisawa 1976. conjecture all 2020 by ...

hey climb walls and scuttle upside down across ceilings, dive to the ocean floor to feed on algae, even glide through the air from treetops. Some, with no limbs and extremely long tails, look like snakes; others are snakes. Many are nearly invisible in their home habitats; others announce their presence to their neighbors and warn off potential rivals by flashing colorful dewlaps, or fanlike st...