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 -