Download - Advanced Counting

Section 7.0 7.0.1

Chapter 7AdvancedCounting

7.1 Recurrence Relations

7.2 Solving Recurrence Relations

7.3 Divide-and-Conquer Relations (abridged)

7.4 Generating Functions

7.5* Inclusion-Exclusion

7.6* Applications of Inclusion-Exclusion

coursenotes by Prof. J. L. Gross for Rosen 6th Edition

Section 7.1 Recurrence Relations 7.1.1

7.1 RECURRENCE RELATIONS


7.1.2 Chapter 7 Advanced Counting

N -AIVE METHOD OF SOLUTION



APPLICATIONS







ADMONITION


Section 7.2Solving Easy Recurrences 7.2.1

7.2 SOLVING EASY RECURRENCES





HOMOG LINEAR RR’s w. CONST COEFF’S



DEGREE ONE, LINEAR HOMOGENEOUS



DEGREE TWO, LINEAR HOMOGENEOUS





DEGREE THREE, LINEAR HOMOGENEOUS



NONHOMOGENEOUS LINEAR RECURRENCES





REPEATED ROOTS


Section 7.3 Divide-and-Conquer Relations 7.3.1

7.3 DIVIDE-AND-CONQUER RELATIONS




Section 7.4 Generating Functions 7.4.1

7.4 GENERATING FUNCTIONS



RATIONAL FUNCTIONS



ENCODING A GIVEN SEQUENCE AS AN OGF







EXTENDED BINOMIAL THEOREM





USING GEN FCNS TO SOLVE RR’s







PARTIAL FRACTIONS




