Name
Abstract | ||
|---|---|---|
In the area of forbidden subposet problems we look for the largest possible size La(n, P) of a family F subset of 2([n]) that does not contain a forbidden inclusion pattern described by P. The main conjecture of the area states that for any finite poset P there exists an integer e(P) such that La(n; P) = (e(P) + o(1)) ((n)([n/2])).In this paper, we formulate three strengthenings of this conjecture and prove them for some specific classes of posets. (The parameters x(P) and d(P) are defined in the paper.)For any finite connected poset P and epsilon > 0, there exists delta > 0 and an integer x(P) such that for any n large enough, and F subset of 2([n]) of size (e(P) + epsilon)((n)([n/2])), F contains at least delta n(x(P)) ((n)([n/2])) copies of P.The number of P-free families in 2([n]) is 2((e(P)+o(1))([n/2]n)).Let P(n; p) be the random subfamily of 2([n]) such that every F is an element of 2([n]) belongs to P(n, p) with probability p independently of all other subsets F' is an element of 2([n]). For any finite poset P, there exists a positive rational d(P) such that if p = omega(n(-d(P))), then the size of the largest P-free family in P(n; p) is (e(P) + o(1))p((n)([n/2])) with high probability. |
Year | DOI | Venue |
|---|---|---|
2021 | 10.37236/9715 | ELECTRONIC JOURNAL OF COMBINATORICS |
DocType | Volume | Issue |
Journal | 28 | 1 |
ISSN | Citations | PageRank |
1077-8926 | 0 | 0.34 |
References | Authors | |
0 | 4 | |
Name | Order | Citations | PageRank |
|---|---|---|---|
| Dániel Gerbner | 1 | 46 | 21.61 |
| Dániel Nagy | 2 | 0 | 0.34 |
| Balázs Patkós | 3 | 85 | 21.60 |
| Máté Vizer | 4 | 27 | 14.06 |