首页|A note on a conjecture of Bene Watts-Norin-Yepremyan for Lagrangian
A note on a conjecture of Bene Watts-Norin-Yepremyan for Lagrangian
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NSTL
Elsevier
What is the maximum Lagrangian of an r-uniform hypergraph that is t-intersecting? For t = 1, the answer is complete; the case r = 3 was determined by Hefetz and Keevash in 2012, and the remaining cases r >= 4 were determined by Bene Watts, Norin and Yepremyan in 2018. For integers n, r, t, i with 1 <= t <= r <= n and 0 <= i <= r t, let F (n, r, t, i) := {e is an element of([n]/r) : |e boolean AND [t + 2i]| >= t + i} be a t-intersecting r-uniform hypergraph. Bene Watts, Norin and Yepremyan further conjectured that if an r-graph G is t-intersecting, then lambda(G) < max lim lambda(F (n, r, t, i))(0 <= i <= r-tn ->infinity). In this paper, we confirm the conjecture for t. {r - 1, r - 2}, and r is an element of {3, 4, 5, 6}. (C) 2022 Elsevier Inc. All rights reserved.
NSTL
Elsevier
