Inequalities for the number of monotonic functions of partial orders

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Let P be a finite poset and let x, y, ∈ P. Let C be a finite chain. Define NS(i, j) to be the number of strict order-preserving maps ω: P → C satisfying ω(x) = i) and ω(y) = j. Various inequalities are proved, commencing with Theorem 2: If r, s, t, u, v, w are non-negative integers then Ns(r, u + v + w)NS(r + s + t, u)⩽NS(r + s, u + w)NS(r + t, u +v). The case v = w = 0 is a theorem of Daykin, Daykin and Paterson, which is an analogue of a theorem of Stanley for linear extensions.
Original languageEnglish
Pages (from-to)41-55
Number of pages15
JournalDiscrete Mathematics
Issue number1
Publication statusPublished - 01 Aug 1986
Externally publishedYes


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