Combinatorics Definition and 398 Threads

  1. D

    A Probability of finding a k-subset in a d-dimensional random

    For a somwehat simple version of the problem, imagine a group of ten people (n=10), for which we observe two binary attributes (d= 2). One of the attributes tells us if any given person wears glasses (d_1) the other if any given person wears a hat (d_2). We know that in total 5 people wear hats...
  2. C

    MHB Some fundamental question in combinatorics

    Hey. We started to study all this subject of combinatorics integrated with the subject of functions. 1. I don't actually understand how to integrate between combinatorics and function, those functions which represent our possibilities and etc... And why at all we need to represent our...
  3. C

    Factoring Combinatorial Functions

    Homework Statement Define {x \choose n}=\frac{x(x-1)(x-2)...(x-n+1)}{n!} for positive integer n. For what values of positive integers n and m is g(x)={{{x+1} \choose n} \choose {m}}-{{{x} \choose n} \choose {m}} a factor of f(x)={{{x+1} \choose n} \choose {m}}? Homework Equations The idea...
  4. D

    I A formula for the number of structures composed of n squares

    Hello, The problem I came up with deals with the structures that can be obtained by joining squares side to side or corner to corner. Specifically to this problem, structures, that are symmetrical to each other, are regarded the same. Ideally, I am looking for a formula that will tell how many...
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    • Forum: General Math
  5. Combinatorics by Dr. L. S. Chandran (NPTEL):- Lecture 01: Pigeon hole principle - (Part 1)

    Combinatorics by Dr. L. S. Chandran (NPTEL):- Lecture 01: Pigeon hole principle - (Part 1)

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  6. Combinatorics by Dr. L. S. Chandran (NPTEL):- Lecture 02: Pigeon hole principle - (Part 2)

    Combinatorics by Dr. L. S. Chandran (NPTEL):- Lecture 02: Pigeon hole principle - (Part 2)

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  7. Combinatorics by Dr. L. S. Chandran (NPTEL):- Lecture 03: Pigeon hole principle - (Part 3)

    Combinatorics by Dr. L. S. Chandran (NPTEL):- Lecture 03: Pigeon hole principle - (Part 3)

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  8. Combinatorics by Dr. L. S. Chandran (NPTEL):- Lecture 04: Pigeon hole principle - (Part 4)

    Combinatorics by Dr. L. S. Chandran (NPTEL):- Lecture 04: Pigeon hole principle - (Part 4)

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  9. Combinatorics by Dr. L. S. Chandran (NPTEL):- Lecture 05: Elementary concepts and basic counting principles

    Combinatorics by Dr. L. S. Chandran (NPTEL):- Lecture 05: Elementary concepts and basic counting principles

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  10. Combinatorics by Dr. L. S. Chandran (NPTEL):- Lecture 06: Elementary concepts; Binomial theorem; Bijective proofs - Part 1

    Combinatorics by Dr. L. S. Chandran (NPTEL):- Lecture 06: Elementary concepts; Binomial theorem; Bijective proofs - Part 1

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  11. Combinatorics by Dr. L. S. Chandran (NPTEL):- Lecture 07: Bijective proofs - Part 2

    Combinatorics by Dr. L. S. Chandran (NPTEL):- Lecture 07: Bijective proofs - Part 2

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  12. Combinatorics by Dr. L. S. Chandran (NPTEL):- Lecture 08: Bijective proofs - Part 3; Properties of binomial coefficients

    Combinatorics by Dr. L. S. Chandran (NPTEL):- Lecture 08: Bijective proofs - Part 3; Properties of binomial coefficients

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  13. Combinatorics by Dr. L. S. Chandran (NPTEL):- Lecture 09: Combinatorial identities - Part (2); Permutations of multisets - Part 1

    Combinatorics by Dr. L. S. Chandran (NPTEL):- Lecture 09: Combinatorial identities - Part (2); Permutations of multisets - Part 1

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  14. Combinatorics by Dr. L. S. Chandran (NPTEL):- Lecture 10: Permutations of multisets - Part 2

    Combinatorics by Dr. L. S. Chandran (NPTEL):- Lecture 10: Permutations of multisets - Part 2

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  15. Combinatorics by Dr. L. S. Chandran (NPTEL):- Lecture 11: Multinomial Theorem, Combinations of Multisets -- Part 1

    Combinatorics by Dr. L. S. Chandran (NPTEL):- Lecture 11: Multinomial Theorem, Combinations of Multisets -- Part 1

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  16. Combinatorics by Dr. L. S. Chandran (NPTEL):- Lecture 12: Combinations of Multisets - Part 2

    Combinatorics by Dr. L. S. Chandran (NPTEL):- Lecture 12: Combinations of Multisets - Part 2

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  17. Combinatorics by Dr. L. S. Chandran (NPTEL):- Lecture 13: Combinations of Multisets - Part 3, Bounds for binomial coefficients

    Combinatorics by Dr. L. S. Chandran (NPTEL):- Lecture 13: Combinations of Multisets - Part 3, Bounds for binomial coefficients

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  18. Combinatorics by Dr. L. S. Chandran (NPTEL):- Lecture 14: Sterling's Formula, Generalization of Binomial coefficients - Part 1

    Combinatorics by Dr. L. S. Chandran (NPTEL):- Lecture 14: Sterling's Formula, Generalization of Binomial coefficients - Part 1

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  19. Combinatorics by Dr. L. S. Chandran (NPTEL):- Lecture 15: Generalization of Binomial coefficients - Part 2

    Combinatorics by Dr. L. S. Chandran (NPTEL):- Lecture 15: Generalization of Binomial coefficients - Part 2

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  20. Combinatorics by Dr. L. S. Chandran (NPTEL):- Lecture 16: Generalization of Binomial coefficients - Part 3; Double counting - Part 1

    Combinatorics by Dr. L. S. Chandran (NPTEL):- Lecture 16: Generalization of Binomial coefficients - Part 3; Double counting - Part 1

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  21. Combinatorics by Dr. L. S. Chandran (NPTEL):- Lecture 17: Double counting - Part 2

    Combinatorics by Dr. L. S. Chandran (NPTEL):- Lecture 17: Double counting - Part 2

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  22. Combinatorics by Dr. L. S. Chandran (NPTEL):- Lecture 18: Hall's Theorem for regular bipartite graphs; Inclusion exclusion principle - Part 1

    Combinatorics by Dr. L. S. Chandran (NPTEL):- Lecture 18: Hall's Theorem for regular bipartite graphs; Inclusion exclusion principle - Part 1

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  23. Combinatorics by Dr. L. S. Chandran (NPTEL):- Lecture 19: Inclusion exclusion principle - Part 2

    Combinatorics by Dr. L. S. Chandran (NPTEL):- Lecture 19: Inclusion exclusion principle - Part 2

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  24. Combinatorics by Dr. L. S. Chandran (NPTEL):- Lecture 20: Inclusion exclusion principle - Part 3

    Combinatorics by Dr. L. S. Chandran (NPTEL):- Lecture 20: Inclusion exclusion principle - Part 3

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  25. Combinatorics by Dr. L. S. Chandran (NPTEL):- Lecture 21: Inclusion exclusion principle - Part 4

    Combinatorics by Dr. L. S. Chandran (NPTEL):- Lecture 21: Inclusion exclusion principle - Part 4

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  26. Combinatorics by Dr. L. S. Chandran (NPTEL):- Lecture 22: Inclusion exclusion principle - Part 5

    Combinatorics by Dr. L. S. Chandran (NPTEL):- Lecture 22: Inclusion exclusion principle - Part 5

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  27. Combinatorics by Dr. L. S. Chandran (NPTEL):- Lecture 23: Recurrence Relations - Part 1

    Combinatorics by Dr. L. S. Chandran (NPTEL):- Lecture 23: Recurrence Relations - Part 1

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  28. Combinatorics by Dr. L. S. Chandran (NPTEL):- Lecture 24: Recurrence Relations - Part 2

    Combinatorics by Dr. L. S. Chandran (NPTEL):- Lecture 24: Recurrence Relations - Part 2

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  29. Combinatorics by Dr. L. S. Chandran (NPTEL):- Lecture 25: Recurrence Relations - Part 3

    Combinatorics by Dr. L. S. Chandran (NPTEL):- Lecture 25: Recurrence Relations - Part 3

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  30. Combinatorics by Dr. L. S. Chandran (NPTEL):- Lecture 26: Recurrence Relations - Part 4

    Combinatorics by Dr. L. S. Chandran (NPTEL):- Lecture 26: Recurrence Relations - Part 4

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  31. Combinatorics by Dr. L. S. Chandran (NPTEL):- Lecture 27: Recurrence Relations - Part 5

    Combinatorics by Dr. L. S. Chandran (NPTEL):- Lecture 27: Recurrence Relations - Part 5

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  32. Combinatorics by Dr. L. S. Chandran (NPTEL):- Lecture 28: Generating functions - Part 1

    Combinatorics by Dr. L. S. Chandran (NPTEL):- Lecture 28: Generating functions - Part 1

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  33. Combinatorics by Dr. L. S. Chandran (NPTEL):- Lecture 29: Generating functions - Part 2

    Combinatorics by Dr. L. S. Chandran (NPTEL):- Lecture 29: Generating functions - Part 2

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  34. Combinatorics by Dr. L. S. Chandran (NPTEL):- Lecture 30: Solving recurrence relations using generating functions - Part 1

    Combinatorics by Dr. L. S. Chandran (NPTEL):- Lecture 30: Solving recurrence relations using generating functions - Part 1

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  35. Combinatorics by Dr. L. S. Chandran (NPTEL):- Lecture 31: Solving recurrence relations using generating functions - Part 2

    Combinatorics by Dr. L. S. Chandran (NPTEL):- Lecture 31: Solving recurrence relations using generating functions - Part 2

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  36. Combinatorics by Dr. L. S. Chandran (NPTEL):- Lecture 32: Exponential generating functions - Part 1

    Combinatorics by Dr. L. S. Chandran (NPTEL):- Lecture 32: Exponential generating functions - Part 1

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  37. Combinatorics by Dr. L. S. Chandran (NPTEL):- Lecture 33: Exponential generating functions - Part 2, Partition Number - Part 1

    Combinatorics by Dr. L. S. Chandran (NPTEL):- Lecture 33: Exponential generating functions - Part 2, Partition Number - Part 1

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  38. Combinatorics by Dr. L. S. Chandran (NPTEL):- Lecture 34: Partition Number - Part 2

    Combinatorics by Dr. L. S. Chandran (NPTEL):- Lecture 34: Partition Number - Part 2

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  39. Combinatorics by Dr. L. S. Chandran (NPTEL):- Lecture 35: Partition Number - Part 3

    Combinatorics by Dr. L. S. Chandran (NPTEL):- Lecture 35: Partition Number - Part 3

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  40. Combinatorics by Dr. L. S. Chandran (NPTEL):- Lecture 36: Partition Number - Part 4; Catalan Numbers - Part 1

    Combinatorics by Dr. L. S. Chandran (NPTEL):- Lecture 36: Partition Number - Part 4; Catalan Numbers - Part 1

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  41. Combinatorics by Dr. L. S. Chandran (NPTEL):- Lecture 37: Catalans Numbers - Part 2

    Combinatorics by Dr. L. S. Chandran (NPTEL):- Lecture 37: Catalans Numbers - Part 2

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  42. Combinatorics by Dr. L. S. Chandran (NPTEL):- Lecture 38: Catalan Numbers - Part 3, Sterling numbers of the 2nd kind

    Combinatorics by Dr. L. S. Chandran (NPTEL):- Lecture 38: Catalan Numbers - Part 3, Sterling numbers of the 2nd kind

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  43. Combinatorics by Dr. L. S. Chandran (NPTEL):- Lecture 39: Difference Sequences

    Combinatorics by Dr. L. S. Chandran (NPTEL):- Lecture 39: Difference Sequences

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  44. Combinatorics by Dr. L. S. Chandran (NPTEL):- Lecture 40: Sterling Numbers

    Combinatorics by Dr. L. S. Chandran (NPTEL):- Lecture 40: Sterling Numbers

    COPYRIGHT strictly reserved to Dr. L. S. Chandran and NPTEL, Govt of India. Duplication prohibited. Lectures: http://www.nptel.ac.in/courses/106108051/ Syllabus: http://www.nptel.ac.in/syllabus/syllabus.php?subjectId=106108051
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    • combinatorics nptel
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  45. Combinatorics by Dr. L. S. Chandran (NPTEL):- Lecture 41: Summary

    Combinatorics by Dr. L. S. Chandran (NPTEL):- Lecture 41: Summary

    COPYRIGHT strictly reserved to Dr. L. S. Chandran and NPTEL, Govt of India. Duplication prohibited. Lectures: http://www.nptel.ac.in/courses/106108051/ Syllabus: http://www.nptel.ac.in/syllabus/syllabus.php?subjectId=106108051
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  46. S

    Efficient way of picking a subset that fulfills criteria

    Let's say there is a set of n elements, S. P is a subset of S, with m elements, and satisfies some conditions, i.e. c1 < f(P) < c2 and g(P) < c3, where f and g are some functions on the elements of P and c1, c2 and c3 are constants. For practical purposes, S is represented as a sorted array of...
  47. ubergewehr273

    Finding no. of combinations for the situation

    Homework Statement Refer the image Homework Equations Equations for permutations and combinations The Attempt at a Solution Let x be the no. of questions that turned out to be correct. So total score will be 3x-(10-x)=4x-10. The value of this expression must be from the given set and since x...
  48. C

    A Combinatorial optimization problem

    Hi, I have the following optimization problem. I have a list of tasks that I should be able to perform with my tools. Each tool costs a certain amount of money, and may be used to carry out a finite number of tasks. The goal is to choose an optimal set of tools in such a way that the toolset can...
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  49. Sarina3003

    Counting Sequences with Repetition Using Stars and Bars Method

    Homework Statement The question is counting how many sequence length 10 with 1,2,3 if a) increasing from left to right with repetition allowed b) increase from left to right with each number appear at least once (still with repetition allowed) Homework Equations It is the stars and bars...
  50. Cathr

    I Combinatorics & probability density

    Suppose we have two boxes, each containing three types of balls. On each ball there's written a number: First box: 1, 2, 3 Second box: 4, 5, 6 We don't know how many balls of each type there are, but we know the probability of taking out a specific one, so that we can make a graph showing the...