We introduce a special type of graph embedding called book embedding and apply it to posets. A book embedding scheme for bipartite graphs is given, and is used to extend the embeddings to general k-partite graphs. Finally, we view the Hasse diagram of a poset as a directed k-partite graph and use this scheme to derive a book embedding for arbitrary posets. Using this book embedding scheme, we a...

The goal of this paper is twofold. First, we give an elementary introduction to the usage of spectral sequences in the combinatorial setting. Second we list a number of applications. In the first group of applications the simplicial complex is the nerve of a poset; we consider general posets and lattices, as well as partition-type posets. Our last application is of a different nature: the Sn-qu...

D denotes the homomorphism poset of finite directed graphs. An antichain duality is a pair 〈F ,D〉 of antichains of D such that (F→) ∪ (→D) = D is a partition. A generalized duality pair in D is an antichain duality 〈F ,D〉 with finite F and D. We give a simplified proof of the Foniok Nešetřil Tardif theorem for the special case D, which gave full description of the generalized duality pairs in D...

Weanalyse the representability of different classes of binary relations on a set bymeans of suitable fuzzy numbers. In particular, we show that symmetric triangular fuzzy numbers can be considered as the best codomain to represent interval orders. We also pay attention to the representability of other classes of acyclic binary relations. © 2005 Elsevier B.V. All rights reserved.

We define a poset of partitions associated to an operad. We prove that the operad is Koszul if and only if the poset is Cohen-Macaulay. In one hand, this characterisation allows us to compute the homology of the poset. This homology is given by the Koszul dual operad. On the other hand, we get new methods for proving that an operad is Koszul.

We study flag enumeration in intervals in the uncrossing partial order on matchings. We produce a recursion for the cd-indices of intervals in the uncrossing poset Pn. We explicitly describe the matchings by constructing an order-reversing bijection. We obtain a recursion for the ab-indices of intervals in the poset P̂n, the poset Pn with a unique minimum 0̂ adjoined.

Codes over various metrics such as Rosenbloom-Tsfasman (RT), Lee, etc. have been considered. Recently, codes over poset metrics have been studied. Poset metric is a great generalization of many metrics especially the well-known ones such as the RT and the Hamming metrics. Poset metric can be realized on the channels with localized error occurrences. It has been shown that MacWilliams identities...

This note corrects and extends a recent axiomatic characterization of the Orlovsky choice function for a particular class of transitive fuzzy relations. The interest of characterizing choice functions for "well-behaved" fuzzy relations is then discussed.