math239-26052008

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

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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

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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

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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 .
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