Tuyển tập các báo cáo nghiên cứu khoa học ngành toán học tạp chí Department of Mathematic dành cho các bạn yêu thích môn toán học đề tài: Value-Peaks of Permutations. | Value-Peaks of Permutations Pierre Bouchard Departement de mathematiques Universite du Quebec à Montreal Case postale 8888 Succursale Centre-ville Montreal Quebec Canada H3C 3P8 Hungyung Chang Department of Applied Mathematics National Sun Yat-sen University Kaohsiung Taiwan 80424 changhy@ Jun Ma Jean Yeh Institute of Mathematics Academia Sinica Taipei Taiwan majun904@ Department of Mathematics National Taiwan University Taipei Taiwan Yeong-Nan Yeh Institute of Mathematics Academia Sinica Taipei Taiwan mayeh@ Submitted Nov 29 2009 Accepted Mar 16 2010 Published Mar 29 2010 Mathematics Subject Classification 05A15 Abstract In this paper we focus on a local property of permutations value-peak. A permutation ơ has a value-peak ơ i if ơ i 1 ơ i ơ i 1 for some i E 2 n 1 . Define VP ơ as the set of value-peaks of the permutation Ơ. For any S c 3 n define VPn S such that VP ơ S. Let Pn S VPn S 0 . we make the set Pn into a poset Pn by defining S Y T if S c T as sets. We prove that the poset Pn is a simplicial complex on the set 3 n and study some of its properties. We give enumerative formulae of permutations in the set VPn S . Partially supported by NSC 98-2115-M-110-009 1 Corresponding author Partially supported by NSC 96-2115-M-001-005 THE ELECTRONIC JOURNAL OF COMBINATORICS 17 2010 R46 1 1 Introduction Let m n m m 1 n . If m n then m n 0. Let n 1 n and n be the set of all the permutations on the set n . We write permutations of n in the form a a 1 a 2 a n . Fix a permutation a in Sn. For every i G n 1 if a i a i 1 then we say that i is a position-descent of a. Define the position-descent set of a permutation a denoted by PD a as PD a i G n 1 a i a i 1 . Given a set S c n 1 suppose PD a S for some a G Sn. We easily obtain the increasing and decreasing intervals of a from the set S. The permutation a is a function from the set n to itself. Since the monotonic property of a .
