组合数学试题2012.docx

哈尔滨工业大学深圳研究生院2012年 秋 季学期期末考试试卷HIT Shenzhen Graduate School Examination PaperCourse Name: 组合数学 Lecturer: 黄荷姣 QuestionOneTwoThreeFourFiveSixSevenEightNineTenTotalMarkThe following formula and results may be useful for you in this examination.The number of ways to place n non-attacking, indistinguishable rooks on an n-by-n board with forbidden positions equals n! – r1(n-1)! + r2(n-2)! - ... + (-1)k rk(n-k)!+…+(-1)rrn.For a specified grid i in chessboard C, let Ci be a chessboard induced from C by deleting the row and the column of grid i；let Ce be induced from C by deleting grid i from C. Then, rk(C)=rk－1(Ci)＋rk(Ce)，R(C)= xR(Ci) + R(C e).Assume that the sequence h0, h1, h2, …, hn,… has a difference table whose 0th diagonal equals, c0, c1, c2, …, cp≠0, 0, 0, … Then, hn = c0 C(n, 0) + c1C(n, 1) + c2C(n, 2) + … +cpC(n, p). and Let n ≥ 2 be an integer. If there exist n-1 MOLS of order n, then there exists a resolvable BIBD with parameters b = n2+n, v = n2, k = n, r = n+1, = 1. , where type(f) = (e1, e2,…,en).Question One: Please give the answers for the following 18 questions without explanation. (3’) A football team of 11 players is to be selected from a set of players, 5 of whom can play only in the back?eld, 8 of them can only play on the line, 2 of them can play either in the back?eld, or on the line. Assuming a football team has 7 men on the line and 4 men in the back?eld, the number of possible football teams is ( ). (3’) Determine an integer mn such that if mn points are chosen within an equilateral triangle of side length 1, there are two whose distance apart is at most . mn = ( )(3’) Consider the permutation of {1,2,3,4,5,6,7,8}. The inversion sequence ofis ( ); The permutation with an inversion sequence is ( ).(3’) In which position does the combination 1289 occur in the lexicographic order of the 4-combinations of {1, 2, 3, 4, 5, 6, 7, 8, 9}? ( ).(3’) Among the combinati