The Book of Poetry : Zhou dynastic building

“Woven” like many of the Da ya (Greater Odes) sings of two of the heroes who laid the groundwork for their grandson and son to overcome the Shang and establish the Zhou dynasty. The text lends itself to memorization and may have been part of early court ritual as our own Star-Spangled Banner celebrates an event in the early history of our country

A note on the least number of edges of 3-uniform hypergraphs with upper chromatic number 2

AbstractThe upper chromatic number χ¯(H) of a hypergraph H=(X,E) is the maximum number k for which there exists a partition of X into non-empty subsets X=X1∪X2∪⋯∪Xk such that for each edge at least two vertices lie in one of the partite sets. We prove that for every n⩾3 there exists a 3-uniform hypergraph with n vertices, upper chromatic number 2 and ⌈n(n-2)/3⌉ edges which implies that a corresponding bound proved in [K. Diao, P. Zhao, H. Zhou, About the upper chromatic number of a co-hypergraph, Discrete Math. 220 (2000) 67–73] is best-possible

Nash equilibria of games with monotonic best replies

We introduce notions of increasingness for the best reply of a game that capture properly the intuitive idea of complementarity among players’ strategies. We show, by generalizing the fixpoint theorems of Veinott and Zhou, that the Nash sets of our games with increasing best replies are nonempty complete lattices. Hence we extend the class of games with strategic complementarities.Complementarity, supermodular games, fixpoint theorem, Nash equilibria