Open AccessOn Jump-Critical Ordered Sets with Jump Number Four
Author(s) -
Elsayed Badr,
Mahmoud I. Moussa
Publication year - 2014
Publication title -
journal of advances in applied and computational mathematics
Language(s) - English
Resource type - Journals
ISSN - 2409-5761
DOI - 10.15377/2409-5761.2014.01.01.2
Subject(s) - jump , mathematics , extension (predicate logic) , successor cardinal , linear extension , combinatorics , set (abstract data type) , discrete mathematics , mathematical analysis , physics , partially ordered set , computer science , quantum mechanics , programming language
For an ordered set P and for a linear extension L of P, let s(P,L) stand for the number of ordered pairs (x, y) of elements of P such that y is an immediate successor of x in L but y is not even above x in P. Put s(P) = min {s(P, L): Llinear extension of P}, the jump number of P. Call an ordered set P jump-critical if s(P - {x}) < s(P) for any x ϵ P. We introduce some theorems about the jump-critical ordered sets with jump number four.