TY - JOUR ID - 36279 TI - Some Results about the Contractions and the Pendant Pairs of a Submodular System JO - Sahand Communications in Mathematical Analysis JA - SCMA LA - en SN - 2322-5807 AU - Hanifehnezhad, Saeid AU - Dolati, Ardeshir AD - Department of Mathematics, Shahed University, Tehran, Iran. AD - Department of Computer Science, Shahed University, Tehran, Iran. Y1 - 2019 PY - 2019 VL - 16 IS - 1 SP - 119 EP - 128 KW - Submodular system KW - Submodular optimization KW - Maximum adjacency ordering KW - Posimodular functions KW - Pendant pairs KW - st-cut DO - 10.22130/scma.2018.91924.481 N2 - Submodularity is an important  property of set functions with deep theoretical results  and various  applications. Submodular systems appear in many applicable area, for example machine learning, economics, computer vision, social science, game theory and combinatorial optimization.  Nowadays submodular functions optimization has been attracted by many researchers.  Pendant pairs of a symmetric submodular system  play  essential role  in finding a minimizer of this system.  In this paper,  we investigate some relations between pendant  pairs of  a  submodular  system and pendant pairs of its contractions. For a symmetric submodular system $\left(V,f\right)$ we construct a suitable sequence of $\left|V\right|-1$ pendant pairs of its contractions. By using this sequence, we present some properties of the system and its contractions. Finally, we prove some results about the minimizers of a posimodular function. UR - https://scma.maragheh.ac.ir/article_36279.html L1 - https://scma.maragheh.ac.ir/article_36279_8d135d8fd6e9c532ae60aff53488a3d6.pdf ER -