ing from the embeddability relation between order types, define a quasi-order to be a reflexive, transitive relation. Throughout this paper, the letters Q and R will range over quasi-ordered sets and classes. Various quasi-ordered spaces will be defined; in each case we will use the symbol < (perhaps with subscripts) to denote the quasi-order under consideration. If q1, q2 E Q, write ql < q2 to...

In this paper, for any two bipartite ordered sets P and Q; we de ne the convolution P Q of P and Q: For dim(P ) = s and dim(Q) = t; we prove that s+ t (U + V ) 2 dim(P Q) s+t (U+V )+2; where U+V is the max-min integer of the certain realizers. In particular, we also prove that dim(Pn;k) = n+k b n+k 3 c for 2 k n < 2k and dim(Pn;k) = n for n 2k; where Pn;k = Sn Sk is the convolution of two stand...

For a fmite ordered set P, let c(P) denote the cardinality of the largest subset Q such that the induced suborder on Q satisfies the Jordan-Dedekind chain condition (JDCC), i.e., every maximal chain in Q has the same cardinality. For positive integers n, let be the minimum of c(P) over all ordered sets P of cardinahty n. We prove: &r 1 <f(n) < 4e AhfS (MOS) subject ckwiflcation (1980). 06AO5.

It is NP-complete to determine whether a given ordered set has a fixed point free orderpreserving self-map. On the way to this result, we establish the NP-completeness of a related problem: Given ordered sets P and Q with t-tuples (PI,. ,pt) and (41,. . , qt) from P and Q respectively, is there an order-preserving map f: P + Q satisfying f(pz) > qr for each i = l,...,t? Mathematics Subject Clas...

The order polytope O(P ) and the chain polytope C(P ) associated to a partially ordered set P are studied. In this paper, we introduce the convex polytope Γ(O(P ),−C(Q)) which is the convex hull of O(P ) ∪ (−C(Q)), where both P and Q are partially ordered sets with |P | = |Q| = d. It will be shown that Γ(O(P ),−C(Q)) is a normal and Gorenstein Fano polytope by using the theory of reverse lexico...

In this paper, we present equivalent characterizations of L-closure systems on lower bounded complete L-ordered sets and complete L-lattices, respectively. These results demonstrate the feasibility of notion of fuzzy closure system developed in our previous work (L.-K. Guo, G.-Q. Zhang, Q.-G. Li: Fuzzy closure systems on L-ordered sets. Math. Log. Quart. 57 (3) (2011), 281-291.). Also we develo...

We consider the semi-infinite q–state Potts model. We prove, for large q, the existence of a first order surface phase transition between the ordered phase and the the so-called “new low temperature phase” predicted in [27], in which the bulk is ordered whereas the surface is disordered.

The large-q expansions of the exponential correlation length and the second moment correlation length for the q-state Potts model in two dimensions are calculated at the first order phase transition point both in the ordered and disordered phases. The expansion coefficients in the ordered and disordered phases coincide in lower orders for both of the two types of the correlation lengths, but th...

For a field k of characteristic zero, we study the field of Noetherian power series, k〈〈tQ〉〉, which consists of maps z : Q → k whose supports are Noetherian (i.e., reverse well-ordered) subsets of Q. There is a canonical valuation LE : k〈〈tQ〉〉 → Q ∪ {−∞} that sends a nonzero series to the maximum element of its support. Given a nonzero polynomial f(x, y) ∈ k[x, y] and a series z ∈ k〈〈tQ〉〉 that ...