TL;DR: If F is finite then the polynomial f has exactly n rational roots, and it is found the exact number of a[email protected]?F^x such that f has n rational Roots, for each n.
TL;DR: Using the lemma, a combinatorial proof is given that the average height of an ordered (plane-planted) tree is approximately twice the average node (vertex) level.
TL;DR: A new counting lemma is proved following the functional approach of Gowers, which complements the sparse regularity lemma of Kohayakawa and Rodl, allowing us to count small graphs in regular subgraphs of a sufficiently pseudorandom graph and to prove sparse extensions of several well-known combinatorial theorems.
TL;DR: In this article, the conditions générales d'utilisation (http://www.compositio.nl/) implique l'accord avec les conditions generales de utilisation, i.e., usage commerciale ou impression systématique, constitutive of an infraction pénale.