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The Pareto dominance relation of a preference profile is (the asymmetric part of) a partial order. For any integer n, the problem of the existence of an n-agent preference profile that generates the given Pareto dominance relation is to investigate the dimension of the partial order. We provide a characterization of a partial order having dimension n in general.
Motivated by generalizing Khovanovs categorification of the Jones polynomial, we study functors $F$ from thin posets $P$ to abelian categories $mathcal{A}$. Such functors $F$ produce cohomology theories $H^*(P,mathcal{A},F)$. We find that CW posets,
For any graded poset $P$, we define a new graded poset, $mathcal E(P)$, whose elements are the edges in the Hasse diagram of P. For any group, $G$, acting on the boolean algebra, $B_n$, we conjecture that $mathcal E(B_n/G)$ is Peck. We prove that the
We consider 3 (weighted) posets associated with a graph G - the poset P(G) of distinct induced unlabelled subgraphs, the lattice Omega(G) of distinct unlabelled graphs induced by connected partitions, and the poset Q(G) of distinct unlabelled edge-su
Toric posets are cyclic analogues of finite posets. They can be viewed combinatorially as equivalence classes of acyclic orientations generated by converting sources into sinks, or geometrically as chambers of toric graphic hyperplane arrangements. I
We consider the problem of determining the maximum order of an induced vertex-disjoint union of cliques in a graph. More specifically, given some family of graphs $mathcal{G}$ of equal order, we are interested in the parameter $a(mathcal{G}) = min_{G