TY - JOUR

T1 - Inequalities for the number of monotonic functions of partial orders

AU - Daykin, Jacqueline W.

N1 - Funding Information:
appreciated. This research was supported in part by the Science and Engineering Research Council.

PY - 1986/8/1

Y1 - 1986/8/1

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=38249038706&partnerID=8YFLogxK

U2 - 10.1016/0012-365X(86)90026-9

DO - 10.1016/0012-365X(86)90026-9

M3 - Article

SN - 0012-365X

VL - 61

SP - 41

EP - 55

JO - Discrete Mathematics

JF - Discrete Mathematics

IS - 1

ER -