A q-analogue of Lehmer's congruence
A quantitative aspect of non-unique factorizations: the Narkiewicz constants II
Let K be an algebraic number field with non-trivial class group G and be its ring of integers. For k ∈ ℕ and some real x ≥ 1, let denote the number of non-zero principal ideals with norm bounded by x such that a has at most k distinct factorizations into irreducible elements. It is well known that behaves, for x → ∞, asymptotically like . In this article, it is proved that for every prime p, , and it is also proved that if and m is large enough. In particular, it is shown that for...
A quantitative ergodic theory proof of Szemerédi's theorem.
A quantum field theoretical representation of Euler-Zagier sums.
A quasi-spectral characterization of strongly distance-regular graphs.
A quasisymmetric function generalization of the chromatic symmetric function.
A rainbow -matching in the complete graph with colors.
A Ramsey treatment of symmetry.
A Ramsey-style extension of a theorem of Erdős and Hajnal
If n, t are natural numbers, μ is an infinite cardinal, G is an n-chromatic graph of cardinality at most μ, then there is a graph X with , |X| = μ⁺, such that every subgraph of X of cardinality < t is n-colorable.
A Ramsey-Type Problem for Paths in Digraphs.
A ramsey-type theorem for multiple disjoint copies of induced subgraphs
Let k and ℓ be positive integers with ℓ ≤ k − 2. It is proved that there exists a positive integer c depending on k and ℓ such that every graph of order (2k−1−ℓ/k)n+c contains n vertex disjoint induced subgraphs, where these subgraphs are isomorphic to each other and they are isomorphic to one of four graphs: (1) a clique of order k, (2) an independent set of order k, (3) the join of a clique of order ℓ and an independent set of order k − ℓ, or (4) the union of an independent set of order ℓ and...
A random graph model for power law graphs.
A random walk on the rook placements on a Ferrers board.
A reciprocity theorem for domino tilings.
A recurrence relation for the “inv" analogue of -Eulerian polynomials.
A Recursive Construction for Room Designs
A recursive construction of 1-rotational Steiner 2-designs.
A recursive construction of asymmetric 1-factorisations.
A recursive relation for weighted Motzkin sequences.
A Reduction of Lattice Tiling by Translates of a Cubical Cluster.