UID:
almahu_9948197953002882
Umfang:
1 online resource (942 pages)
ISBN:
9781118557938
,
111855793X
Serie:
ISTE
Inhalt:
How many ways do exist to mix different ingredients, how many chances to win a gambling game, how many possible paths going from one place to another in a network? To this kind of questions Mathematics applied to computer gives a stimulating and exhaustive answer. This text, presented in three parts (Combinatorics, Probability, Graphs) addresses all those who wish to acquire basic or advanced knowledge in combinatorial theories. It is actually also used as a textbook.
Anmerkung:
5.7.3. Language of words made from arrangements taken from n distinct and non-repeated letters a, b, c, etc., where these words are shorter than or equal to n.
,
Cover; Mathematics for Informatics and Computer Science; Title Page; Copyright Page; Table of Contents; General Introduction; Chapter 1. Some Historical Elements; 1.1. Yi King; 1.2. Flavor combinations in India; 1.3. Sand drawings in Africa; 1.4. Galileo's problem; 1.5. Pascal's triangle; 1.6. The combinatorial explosion: Abu Kamil's problem, the palm grove problem and the Sudoku grid; 1.6.1. Solution to Abu Kamil's problem; 1.6.2. Palm Grove problem, where N = 4; 1.6.3. Complete Sudoku grids; PART 1. COMBINATORICS; Part 1. Introduction; Chapter 2. Arrangements and Combinations.
,
2.1. The three formulae2.2. Calculation of Cnp, Pascal's triangle and binomial formula; 2.3. Exercises; 2.3.1. Demonstrating formulae; 2.3.2. Placing rooks on a chessboard; 2.3.3. Placing pieces on a chessboard; 2.3.4. Pascal's triangle modulo k; 2.3.5. Words classified based on their blocks of letters; 2.3.6. Diagonals of a polygon; 2.3.7. Number of times a number is present in a list of numbers; 2.3.8. Words of length n based on 0 and 1 without any block of 1s repeated; 2.3.9. Programming: classification of applications of a set with n elements in itself following the form of their graph.
,
2.3.10. Individuals grouped 2×2Chapter 3. Enumerations in Alphabetical Order; 3.1. Principle of enumeration of words in alphabetical order; 3.2. Permutations; 3.3. Writing binary numbers; 3.3.1. Programming; 3.3.2. Generalization to expression in some base B; 3.4. Words in which each letter is less than or equal to the position; 3.4.1. Number of these words; 3.4.2. Program; 3.5. Enumeration of combinations; 3.6. Combinations with repetitions; 3.7. Purchase of P objects out of N types of objects; 3.8. Another enumeration of permutations; 3.9. Complementary exercises.
,
3.9.1. Exercise 1: words with different successive letters3.9.2. Exercise 2: repeated purchases with a given sum of money; 3.10. Return to permutations; 3.11. Gray code; Chapter 4. Enumeration by Tree Structures; 4.1. Words of length n, based on N letters 1, 2, 3 ..., N, where each letter is followed by a higher or equal letter; 4.2. Permutations enumeration; 4.3. Derangements; 4.4. The queens problem; 4.5. Filling up containers; 4.6. Stack of coins; 4.7. Domino tiling a chessboard; Chapter 5. Languages, Generating Functions and Recurrences; 5.1. The language of words based on two letters.
,
5.2. Domino tiling a 2xn chessboard5.3. Generating function associated with a sequence; 5.4. Rational generating function and linear recurrence; 5.5. Example: routes in a square grid with rising shapes without entanglement; 5.6. Exercises on recurrences; 5.6.1. Three types of purchases each day with a sum of N dollars; 5.6.2. Word building; 5.7. Examples of languages; 5.7.1. Language of parts of an element set {a, b, c, d ... }; 5.7.2. Language of parts of a multi-set based on n elements a, b, c, etc., where these elements can be repeated as much as we want.
Weitere Ausg.:
Print version: Audibert, Pierre. Mathematics for Informatics and Computer Science. London : Wiley, ©2013 ISBN 9781848211964
Sprache:
Englisch
Schlagwort(e):
Electronic books.
;
Electronic books.
;
Electronic books.
URL:
https://onlinelibrary.wiley.com/doi/book/10.1002/9781118557938
URL:
https://onlinelibrary.wiley.com/doi/book/10.1002/9781118557938
URL:
https://onlinelibrary.wiley.com/doi/book/10.1002/9781118557938
