co.combinatorics

  1. Factoring a positive semidefinite matrix into binary matrices

  2. An extension of the Izergin-Korepin determinant to the eight-vertex model

  3. Asymptotic for number of partitions of $n$ into $k$ squares, uniform in $n,k \to +\infty$

  4. Find the probability that two people have talked to each other
  5. dividing a square into unique rectangles with the same perimeter

  6. Is there a natural relationship between OEIS A127670 and Cayley's tree formula?

  7. Twisted graph duplication

  8. Klarner's theorem
  9. Can this sum be majorized?

  10. Triangulations of convex surfaces

  11. A funny kind of Ramsey number

  12. On CNF forms with weight $d$ satisfying instances
  13. How to prove the following inequality?
  14. An explicit formula for the number of different (non isomorphic) simple graphs with $p$ vertices and $q$ edges
  15. A discrete operator begets even/odd polynomials
  16. These polynomials are always either even or odd

  17. What is currently known or conjectured about q,t-Kostka polynomials?
  18. Generating Uniquely k-Optimal Point Sets
  19. Combinatorial/probabilistic statements having $F_{un}$/$F_q$ geometric interpetation
  20. Is there a non-atomic finite positive measure in the plane, of which uncountably many projections have atoms?

  21. Finding a semi-sparse vertex in a grid

  22. Constructive proof of a rational version of Perron-Frobenius?

  23. An extremal sum for hypergraph degrees
  24. Tileability and computabilty

  25. A direct proof that every $r$-colored complete graph on $n=(r+1)m-(r-1)$ vertices has a monochromatic matching of size $m$?

  26. Least number of vertices in a graph with which one can uniquely recover some partition of N

  27. Is this totally unimodular family?
  28. What breaks down in the theory of affine hyperplane arrangments?
  29. Sparse graphs that are hard to color
  30. Number of bipartite graphs with a neighborhood property

  31. How many operad structures are there on the symmetric sequence of simplices / finitely-supported probability measures?

  32. Bichromatic pencils

  33. Does knight behave like a king in his infinite odyssey?

  34. Cycles in the hyperoctahedral group (symmetries of the hypercube)

  35. Choosing $K$ "centers" from the space of permutations
  36. How to label a tree with minimum cost?

  37. Is there a lift of the q-Vandermonde identity to some geometric (motivic) identity for Grassmannians over $F_q$?
  38. Sparse distibuting of n distinct balls into k distinct boxes

  39. What is the minimal $C_k$, such that every $f\colon \{-1,1\}^n\to \mathbb{R}$ of degree at most $k$ satisfies $\|f\|_2\le C_k\|f\|_1$
  40. A lattice ordered by inclusion and isomorphic to the lattice of quotient groups of a finite group
  41. H-generalized join graph

  42. The infinite X in Conway's game of life

  43. Determinant of the oriented adjacency matrix of a tree

  44. The arithmetic progression game and its variations: can you find optimal play?

  45. Clique number for hypergraphs
  46. Number of alternating variations

  47. Generating function for number of r-disjoint subsets each of size k

  48. Congruences Ramanujan-style
  49. How many rich directions a set in $\mathbb F_p^2$ determines?

  50. convex polytope integer points

  51. Does there exist any analogous result for site percolation?

  52. Coefficients of shifted Bernoulli polynomials

  53. Bounds on degrees of minors obtained by edge contractions of regular graphs

  54. Dominance relation among Cartan matrices implies containment of root systems: Is this known?
  55. Minimum number of balls to obtain accurate information about a bipartition of the bin set
  56. Is 3-coloring bounded degree graphs subexponential: $O(\exp{(\sqrt{n}\log^2{n})})$?
  57. Maximum intersecting set families of $\{1,\ldots,n\}$

  58. Proof and interpretation of the following percolation theory result for $n\times n$ square grid
  59. Basis of coinvariant algebra on which reflection group acts as regular representation
  60. Full-rank factorization property of integer-valued matrices
  61. Some strange multinomial averaging
  62. Is Friedman's TREE function the fastest-growing hierarchy and is the growing constant?
  63. There are $n$ horses. At a time only $k$ horses can run in a single race. What is the minimum number of races required to find the $m$ fastest horses?
  64. Minimal Subset Sum Superset

  65. Can this particular random matrix model be converted/related to any existing graph theory model?
  66. Conjecture on palindromic numbers
  67. Improved estimates of $n$ quantities via $n$ measurements

  68. Several convex polytopes in a simplex; fix an extreme point for each; how many can be supported by a function monotonic on all line segments?

  69. simplementability
  70. Regular unimodular triangulation for a certain simplex

  71. A stronger version of the Erdös-Faber-Lovasz conjecture?

  72. Transforming random variables for having good property?

  73. List Ramsey numbers?

  74. Some divisibility constraints in Frobenius coin problem
  75. Birthday Inequality for non uniform distribution with specific collision entropy

  76. New edge coloring problem in graph theory

  77. Is the Erdős–Rényi giant component result applicable here?
  78. Minimum number of operations necessary to arrive at any configuration
  79. Limit of a Combinatorial Function

  80. Natural bijection between Dyck paths and tilting modules
  81. Unique Lowest Common Ancestor

  82. Finding all closed walks on a graph that traverse vertices a given number of times

  83. Some more binomial coefficient determinants

  84. Alice and Bob playing on a circle

  85. Some binomial coefficient determinants

  86. Combinatorial model for twisted involutions in $S_n$

  87. Off-line load in the balls-and-bins problem

  88. Combinatorial optimization problem for bipartite graphs

  89. Lifting matrices mod 2 to integers.
  90. T-equivariant homology of affine Grassmannian
  91. Alternative parallel paths

  92. An upper bound for the number of non-isomorphic graphs having exactly $m$ edges and no isolated vertices
  93. How many simplicial complexes on n vertices up to homotopy equivalence?

  94. Generating function of a sequence involving reciprocals of binomial coefficients

  95. Number of collinear ways to fill a grid
  96. How much of the plane is 4-colorable?

  97. Is the Ford-Fulkerson algorithm a tropical rational function?
  98. Independent decomposition of coordinate distribution

  99. A conjecture about multinomial coefficient

  100. Probability in $GL_2(\mathbb{Z}/p^{r}\mathbb{Z})$