林延輯周鈺偵Chou, Yu-Jen2019-09-052019-07-032019-09-052019http://etds.lib.ntnu.edu.tw/cgi-bin/gs32/gsweb.cgi?o=dstdcdr&s=id=%22G0505401113%22.&%22.id.&http://rportal.lib.ntnu.edu.tw:80/handle/20.500.12235/101500In this thesis, we extend the work of fixed points on the permutations of [n] in two directions: firstly, we discuss the fixed points problems of hyperoctahedral groups Bn; secondly, elements in Bn can be thought the letters are painted by two colors, it can be generalized with r colors. Moreover, we discuss the fixed point problems in the subsets alternating permutations of Bn and strictly decreasing permutations with r colors. After removing all fixed points and standardizing the remaining letters, we focus on colored permutations with 0 or 1 fixed point. We obtain combinatorial correspondence between derangements and elements with exactly one fixed point together with their recursions and generating functions.derangementshyperoctahedral groupsalternating permutationscolored permutations