Some Problems in Combinatorics

@inproceedings{Srinivasan2004SomePI,
  title={Some Problems in Combinatorics},
  author={Murali K. Srinivasan},
  year={2004}
}
Let In = {1, 2, . . . , n} and x : In 7→ R be a map such that ∑ i∈In x(i) ≥ 0. (For any i, its image is denoted by x(i).) Let F = {J ⊂ In : |J | = k, and ∑ j∈J x(j) ≥ 0}. In [25] Manickam and Singhi have conjectured that |F| ≥ ( n−1 k−1 ) whenever n ≥ 4k and showed that the conclusion of the conjecture holds when k divides n. For any two integers r and ` let [r]` denote the smallest positive integer congruent to r (mod `). In [11] Bier and Manickam have shown that if k > 3 and n ≥ k(k − 1)(k… CONTINUE READING