math239-26052008

# Example how many k subsets of 1 n contain no two

This preview shows pages 4–8. Sign up to view the full content.

Useful for studying other combinatorial objects. Example : How many k -subsets of { 1 , . . . , n } contain no two consecutive integers? (Problem 2.3.1) Section 1 (C. Sloss) MATH 239: May 26, 2008

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
Introduction to Binary Strings Unique generation Motivation Definitions 2. Binary Strings as a First Step The study of binary strings generalizes to studying sequences over larger “alphabets,” e.g. { A , C , G , T } . Section 1 (C. Sloss) MATH 239: May 26, 2008
Introduction to Binary Strings Unique generation Motivation Definitions 3. Definition of Binary Strings Definition : A binary string is a finite sequence a 1 a 2 · · · a n , where a i ∈ { 0 , 1 } . The integer n is called the length of the string. w ( a 1 · · · a n ) = n is the usual weight function on binary strings. There is a single string of length 0, called the empty string , denoted by . Section 1 (C. Sloss) MATH 239: May 26, 2008

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
Introduction to Binary Strings Unique generation Motivation Definitions 4. Operations on Binary Strings Let a = a 1 · · · a n and b = b 1 · · · b m be binary strings. The concatenation of a and b is the binary string ab := a 1 · · · a n b 1 · · · b m .
This is the end of the preview. Sign up to access the rest of the document.

{[ snackBarMessage ]}

### What students are saying

• As a current student on this bumpy collegiate pathway, I stumbled upon Course Hero, where I can find study resources for nearly all my courses, get online help from tutors 24/7, and even share my old projects, papers, and lecture notes with other students.

Kiran Temple University Fox School of Business ‘17, Course Hero Intern

• I cannot even describe how much Course Hero helped me this summer. It’s truly become something I can always rely on and help me. In the end, I was not only able to survive summer classes, but I was able to thrive thanks to Course Hero.

Dana University of Pennsylvania ‘17, Course Hero Intern

• The ability to access any university’s resources through Course Hero proved invaluable in my case. I was behind on Tulane coursework and actually used UCLA’s materials to help me move forward and get everything together on time.

Jill Tulane University ‘16, Course Hero Intern