TY - JOUR AU - E.M. Badr, AU - M.I. Moussa, PY - 2014/10/10 Y2 - 2024/03/28 TI - On Jump-Critical Ordered Sets with Jump Number Four JF - Journal of Advances in Applied & Computational Mathematics JA - J. Adv. App. Comput. Math. VL - 1 IS - 1 SE - Articles DO - 10.15377/2409-5761.2014.01.01.2 UR - https://www.avantipublishers.com/index.php/jaacm/article/view/55 SP - 8-13 AB - <p>For an ordered set <em>P</em> and for a linear extension <em>L</em> of <em>P</em>, let s(<em>P,L</em>) stand for the number of ordered pairs (<em>x, y</em>) of elements of <em>P</em> such that <em>y</em> is an immediate successor of <em>x</em> in <em>L</em> but <em>y</em> is not even above <em>x</em> in <em>P</em>. Put <em>s</em>(<em>P</em>) = min {<em>s</em>(<em>P, L</em>): Llinear extension of <em>P</em>}, the jump number of <em>P</em>. Call an ordered set <em>P</em> jump-critical if <em>s</em>(<em>P</em> - {<em>x</em>}) &lt; <em>s</em>(<em>P</em>) for any <em>x </em>ϵ <em>P</em>. We introduce some theorems about the jump-critical ordered sets with jump number four.</p> ER -