catalan numbers - Sweet Briar College
... Figure 4: Examples of Hasse diagrams to illustrate posets. A Hasse diagram is used to represent a finite poset. Each element in the poset is a vertex in the Hasse diagram. The transitive relation in the poset is represented by lines going up from one vertex to another in the Hasse diagram. The lines ...
... Figure 4: Examples of Hasse diagrams to illustrate posets. A Hasse diagram is used to represent a finite poset. Each element in the poset is a vertex in the Hasse diagram. The transitive relation in the poset is represented by lines going up from one vertex to another in the Hasse diagram. The lines ...
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... Most of the distributive lattices we have been considering have an interesting property which we call a "cover characterization." A ^-distributive lattice L is said to have a cover characterization if there exists a function f(k,n) such that if an element x of L of rank k covers/? elements, t h e n ...
... Most of the distributive lattices we have been considering have an interesting property which we call a "cover characterization." A ^-distributive lattice L is said to have a cover characterization if there exists a function f(k,n) such that if an element x of L of rank k covers/? elements, t h e n ...
Finite and Infinite Sets. Countability. Proof Techniques
... Now, I have named the sets A1, A2, … which means that I have implicitly ordered them in some way. However is this always possible? Let us consider the set R = {A1, A2, … Ak, …} This is an infinite set. It may be countable, or it may be not countable. Only if the set is countable, we can order the se ...
... Now, I have named the sets A1, A2, … which means that I have implicitly ordered them in some way. However is this always possible? Let us consider the set R = {A1, A2, … Ak, …} This is an infinite set. It may be countable, or it may be not countable. Only if the set is countable, we can order the se ...
Lesson 5.2 Properties of Functions Exercises (pages 270–273) A 4
... 5. a) Each ordered pair has a different first element, so for every first element there is exactly one second element. So, the relation is a function. The domain is: {1, 2, 3, 4} The range is: {3, 6, 9, 12} b) The ordered pairs (0, 1) and (0, –1) have the same first element, 0. So, the relation is n ...
... 5. a) Each ordered pair has a different first element, so for every first element there is exactly one second element. So, the relation is a function. The domain is: {1, 2, 3, 4} The range is: {3, 6, 9, 12} b) The ordered pairs (0, 1) and (0, –1) have the same first element, 0. So, the relation is n ...
1 Basic Combinatorics
... Principle 1 (The Multiplication Principle) The number of sequences (x1 , x2 , . . . , xk ) such that there are ai choices for xi after having chosen x1 , x2 , . . . , xi−1 for each i = 1, 2, . . . , n is exactly a1 a2 . . . an . The proofs of Theorems 1, 2 and 3 come from this principle. Our argume ...
... Principle 1 (The Multiplication Principle) The number of sequences (x1 , x2 , . . . , xk ) such that there are ai choices for xi after having chosen x1 , x2 , . . . , xi−1 for each i = 1, 2, . . . , n is exactly a1 a2 . . . an . The proofs of Theorems 1, 2 and 3 come from this principle. Our argume ...
section 1.1 solutions
... not well defined, whether a dog is goofy or not is an opinion and different people may classify dogs differently. 11) D is the set of numbers whose square is 16. Answer: Yes I can create an equation and use Algebra to find the elements of the set. The elements are 4 and -4. 13) The set of years that ...
... not well defined, whether a dog is goofy or not is an opinion and different people may classify dogs differently. 11) D is the set of numbers whose square is 16. Answer: Yes I can create an equation and use Algebra to find the elements of the set. The elements are 4 and -4. 13) The set of years that ...
Session 3 - Full glossary of maths terms to be used in both
... students/parents/teachers of the vocabulary and meaning of terms in mathematics that students may have encountered in primary school and will encounter when they transfer to post-primary education. Many of these terms are used throughout the strands in junior cycle, but it is not a comprehensive lis ...
... students/parents/teachers of the vocabulary and meaning of terms in mathematics that students may have encountered in primary school and will encounter when they transfer to post-primary education. Many of these terms are used throughout the strands in junior cycle, but it is not a comprehensive lis ...
