A game of composing binary relations
We investigate the extremal function which, for a given finite sequence over symbols, is defined as the maximum length of a sequence of integers such that 1) , 2) implies and 3) contains no subsequence of the type . We prove that is very near to be linear in for any fixed of length greater than 4, namely that Here is the length of and is the inverse to the Ackermann function and goes to infinity very slowly. This result extends the estimates in [S] and [ASS] which...
A category generalizing Jaeger-Nomura algebra associated to a spin model is given. It is used to prove some equivalence among the four conditions by Jaeger-Nomura for spin models of index 2.
In this paper we generalize the Pascal triangle and examine the connections among the generalized triangles and powering integers respectively polynomials. We emphasize the relationship between the new triangles and the Pascal pyramids, moreover we present connections with the binomial and multinomial theorems.