4:["$","div",null,{"className":"min-h-screen bg-white flex flex-col","children":[["$","div",null,{"className":"px-6 pt-6 pb-4 border-b border-gray-100","children":[["$","div",null,{"className":"flex items-center gap-1.5 text-xs text-gray-400 mb-4","children":[["$","a",null,{"href":"/","className":"hover:text-[#26a69a] transition-colors","children":"Market"}],["$","span",null,{"children":"›"}],["$","span",null,{"className":"text-gray-600","children":"Multitree"}]]}],["$","div",null,{"className":"text-[10px] text-gray-400 uppercase tracking-widest mb-1","children":"Company Profile"}],["$","h1",null,{"className":"text-2xl font-bold text-gray-900","children":"Multitree"}],null]}],["$","div",null,{"className":"flex-1 px-6 py-6","children":[["$","p",null,{"className":"text-sm text-gray-600 leading-relaxed mb-8","children":"In combinatorics and order theory, a multitree may describe either of two equivalent structures: a directed acyclic graph (DAG) in which there is at most one directed path between any two vertices, or equivalently in which the subgraph reachable from any vertex induces an undirected tree, or a partially ordered set (poset) that does not have four items a, b, c, and d forming a diamond suborder with a ≤ b ≤ d and a ≤ c ≤ d but with b and c incomparable to each other."}],["$","div",null,{"className":"columns-1 md:columns-2 gap-10","children":[["$","div","0",{"className":"mb-8 break-inside-avoid","children":[["$","div",null,{"className":"text-xs font-semibold text-gray-400 uppercase tracking-wide mb-3 border-b border-gray-100 pb-1","children":"Equivalence between DAG and poset definitions"}],["$","div",null,{"className":"text-sm text-gray-600 leading-relaxed wiki-content","dangerouslySetInnerHTML":{"__html":"In a directed acyclic graph, if there is at most one directed path between any two vertices, or equivalently if the subgraph reachable from any vertex induces an undirected tree, then its reachability relation is a diamond-free partial order. Conversely, in a diamond-free partial order, the transitive reduction identifies a directed acyclic graph in which the subgraph reachable from any vertex induces an undirected tree. == Diamond-free families =="}}]]}],["$","div","1",{"className":"mb-8 break-inside-avoid","children":[["$","div",null,{"className":"text-xs font-semibold text-gray-400 uppercase tracking-wide mb-3 border-b border-gray-100 pb-1","children":"Diamond-free families"}],["$","div",null,{"className":"text-sm text-gray-600 leading-relaxed wiki-content","dangerouslySetInnerHTML":{"__html":"A diamond-free family of sets is a family F of sets whose inclusion ordering forms a diamond-free poset. If D(n) denotes the largest possible diamond-free family of subsets of an n-element set, then it is known that :2\\le \\lim_{n\\to\\infty} D(n) \\Big/ \\binom{n}{\\lfloor n/2\\rfloor}\\le 2\\frac{3}{11}, and it is conjectured that the limit is 2. == Related structures =="}}]]}],["$","div","2",{"className":"mb-8 break-inside-avoid","children":[["$","div",null,{"className":"text-xs font-semibold text-gray-400 uppercase tracking-wide mb-3 border-b border-gray-100 pb-1","children":"Related structures"}],["$","div",null,{"className":"text-sm text-gray-600 leading-relaxed wiki-content","dangerouslySetInnerHTML":{"__html":"A polytree, a directed acyclic graph formed by orienting the edges of an undirected tree, is a special case of a multitree. The subgraph reachable from any vertex in a multitree is an arborescence rooted in the vertex, that is a polytree in which all edges are oriented away from the root. The word \"multitree\" has also been used to refer to a series–parallel partial order, or to other structures formed by combining multiple trees. == References =="}}]]}]]}],"$Lf"]}],"$L10"]}]