Bounds for the Jump Number of Partially Ordered Sets
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چکیده
A linear extension of a partial order P is a linear order L = x1, x2..., xn respecting the order relations of P , i.e. xi < xj implies i < j for all xi, xj ∈ P . In other words, L is the linear sum L = C0 ⊕ C1 ⊕ . . .⊕ Cm of disjoint chains C0, C1, . . . , Cm in P , whose union is all of P , such that x ∈ Ci, x ′ ∈ Cj and x < x ′ implies i ≤ j. We may assume the chains to be maximal, i.e. the last element of Ci, maxCi, is noncomparable with the first element of Ci+1, minCi+1. The pairs (maxCi,minCi+1) then are the jumps of P . The number of jumps of L is denoted by sP (L) and the jump number of P is
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تاریخ انتشار 1991