combinatorics

  1. What is the largest planar clique in n-dimensions?

  2. Hilbert scheme of $n$ point action, torus action fixed points
  3. Residues of a function with two different essential singularities

  4. How many ways in total that $10$ people can enter the room?
  5. Combinatorics question - Parking Cars

  6. In how many ways can a test be passed with just $10$ right answers if at least $4$ right answers must be from part A of the test?

  7. Trouble interpreting a generating function equation

  8. In how many combination can I deal 6 cards with only 2 numbers on them

  9. Example of a symmetric BBID that is not isomorphic to its dual

  10. Integer solutions with subtraction
  11. Attempting a combinations question using permutations.
  12. closure and circuit of a matroid
  13. Find recurrence relation for two different signals
  14. Combinatorics question, combinations involved in filling up of vacancies.
  15. Number of snake configurations in simple snake game

  16. Show that $\binom{n}{1} + 6\binom{n}{2} + 6\binom{n}{3} = n^3$

  17. Calculate $(-1)^k \left(\begin{matrix} -1/2 \\ k\end{matrix}\right)$. Is it equal to $\frac {(2k)!}{2^{2k}(k!)^2}$?
  18. In how many ways can $3$ red, $3$ blue, and $3$ green balls be arranged so that no two balls of the same colour are consecutive (up to symmetry)?
  19. Exponential Generating Function for the number of sequences in A,B,C

  20. Union of pairwise almost disjoint sets

  21. Prove that $\sum_{i=0}^d {n\choose i}\leq n^d +1$

  22. In how many ways can 10 students be grouped into 2 groups?

  23. Distribution of the Number of Distinct Items in a Sequence of Independent Random Variables

  24. Arithmetic error in Feller's Introduction to Probability?

  25. Number of teams

  26. Optimal Matching Distance

  27. In how many ways can a, b, c, d be formed based on the rule in this problem?

  28. Cauchy's one-line notation for sum over ordered permutations.

  29. Question regarding the Sauer Lemma?

  30. Given an alphabet with three letters a, b, c. Find the number of words of n letters which contain an even number of a's.
  31. Pigeon Hole Principle: 10 balls are partitioned to 5 people, someone has sum over 11
  32. Area of occluded carpets
  33. Partition a square into sub-rectangles with restrictions

  34. Why are urns so common in combinatorics questions?

  35. What does 2 to the power x mean in set theory

  36. How can I prove, that this formula is related to the binomial series?

  37. Difference between these combinatorics questions?

  38. How can we simplify this sum over sets expression?

  39. 1 - Combinatorics - High School Level Olympiad Problem
  40. Combinations for 6-card pattern from 4-deck cards

  41. How to calculate the probability of $3$ heads out of $10$ coins IF each coin has a different probability for head
  42. Finding circles on lattice points with arbitrary origin.

  43. Ways in which number of flags can be generated.

  44. Substring repetitions in integer coloring

  45. Vice-versa Erdos conjecture

  46. $0$ interior to the convex hull of rational vectors

  47. Direct formula to calculate the sum.

  48. Bijection between perfect matchings permutations with even cycles
  49. What is wrong with this counting approach?

  50. Identifying distinct colored cubes from faces of $2 \times 2 \times 2$ arrangement
  51. Suit a problem to the equation $\sum_{i=0}^{n} (-1)^{i} {n \choose i} = 0$

  52. Probability of an element to appear in a different set after permutation.

  53. Counting all $9 \times 8$ matrices with two restrictions (checking if I'm right)

  54. Counting number of paths on a triangular lattice

  55. Finding values of a binary operation defined on N.

  56. How many pizzas possible?

  57. Ternary String Bayes Rule

  58. What is maximum probability of getting some set inside a Generalized Arithmetic Progression?
  59. What is the probability of getting at least one pair in Poker?

  60. In how many ways can $7$ white-suited and $5$ black-suited people be seated at a round table if none of the black-suited people are adjacent?
  61. How many different rows can we make?

  62. Characteristic polynomial of a classical arrangement of hyperplanes.

  63. What is the number of ways to distribute 14 identical balls in 3 numbered boxes, given that there has to be 8 balls in at least one of the boxes?

  64. Different approach to classic pigeonhole principle problem yields different results. Why?

  65. What is the number of ways to divide a rectangle into $n$ smaller rectangles line by line?

  66. John's Circular Table (Combinatorics)

  67. How to find the number of permutations of the letters of the word MATHEMATICS that begin with a consonant

  68. How many permutations are there of the letters in word: Statistics?, with restriction.

  69. How many different sets of tickets are there?

  70. Why ${n \choose k} = {n \choose n-k}$?
  71. Colouring A Cube
  72. Graph Colouring
  73. Probability Problem with $10$ players being put on two teams
  74. If I pull red and blue balls from a bag and place them in order, what is the expected greatest distance between two red balls?

  75. Range numbers combination count.

  76. In how many ways can $4$ of $100$ people sitting at a circular table be selected so that no two of them are adjacent?

  77. Find s, which solves inequality
  78. Derive formula for number of tilings of an $m \times n$ board.

  79. Birthday Problem counting principles

  80. Reference for combinatorial game theory.
  81. Generating fuctions: $\sum_{k=0}^\infty \binom{2k}{k}\binom{n}{k}\left(-\frac{1}{4}\right)^k=2^{-2n}\binom{2n}{n}$

  82. Proof of $\sum_{k=1}^n \binom{n}{k} \binom{n}{n+1-k} = \binom{2n}{n+1}$ via induction

  83. Problem Evaluating a Combinatorics Problem - answer not matching the book

  84. Expected value of exactly one ball in n balls in n boxes

  85. Is there a closed-form expression for Shapley value of glove game?
  86. Counting Multi-Sets for Donuts
  87. How many different 4x4 windows can you create if you only have two colors?
  88. number of acyclic graphs on $n$ vertices having $n-m$ edges

  89. Recurrences which involve polynomials with discriminant $d=11,19,43,67,163$
  90. Good Combinatorics book
  91. Find the joint probability function of $Y_{1}$ and $Y_{2}$

  92. How to determine the size of the complete game tree for basic [M]?

  93. Evaluate the sum $\sum_{k=1}^n {n \choose k-1} {n \choose k}$

  94. Number of ways of seating boys and girls around a table such that two particular boys always sit together and no two girls sit together
  95. Calculate unique combinations for unique guests per table contraint

  96. Ordinary Generating functions that occurs at most 3 times

  97. Inclusion Exclusion Principle Example
  98. Calculating the number of ways a surjective function can be defined.

  99. A simple counting problem
  100. Probability question - rolling dice