Growth rates for subclasses of Av(321).
Hayman admissible functions in several variables.
Hereditary properties of graphs: Asymptotic enumeration, global structure, and colouring.
Improved bounds for the number of forests and acyclic orientations in the square lattice.
Improved upper bounds for self-avoiding walks in .
Independent sets on path-schemes.
Intersections of randomly embedded sparse graphs are Poisson.
-functions of automorphic forms and combinatorics: Dyck paths
We give a combinatorial interpretation for the positive moments of the values at the edge of the critical strip of the -functions of modular forms of and . We deduce some results about the asymptotics of these moments. We extend this interpretation to the moments twisted by the eigenvalues of Hecke operators.
Local limit approximations for Lagrangian distributions.
Locally restricted compositions. I. Restricted adjacent differences.
Locally restricted compositions. II: General restrictions and infinite matrices.
Locally restricted compositions. III: Adjacent-part periodic inequalities.
Longest alternating subsequences in pattern-restricted permutations.
Longest increasing subsequences in pattern-restricted permutations.
Meet and join within the lattice of set partitions.
Multivariate asymptotics for products of large powers with applications to Lagrange inversion.
Odd cutsets and the hard-core model on
We consider the hard-core lattice gas model on and investigate its phase structure in high dimensions. We prove that when the intensity parameter exceeds , the model exhibits multiple hard-core measures, thus improving the previous bound of given by Galvin and Kahn. At the heart of our approach lies the study of a certain class of edge cutsets in , the so-called odd cutsets, that appear naturally as the boundary between different phases in the hard-core model. We provide a refined combinatorial...
On a balanced property of derangements.
On an integer sequence related to a product of trigonometric functions, and its combinatorial relevance.
On averages of randomized class functions on the symmetric groups and their asymptotics
The second author had previously obtained explicit generating functions for moments of characteristic polynomials of permutation matrices ( points). In this paper, we generalize many aspects of this situation. We introduce random shifts of the eigenvalues of the permutation matrices, in two different ways: independently or not for each subset of eigenvalues associated to the same cycle. We also consider vastly more general functions than the characteristic polynomial of a permutation matrix, by...