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We give a combinatorial interpretation for the positive moments of the values at the edge of the critical strip of the $L$ -functions of modular forms of $G L (2)$ and $G L (3)$ . 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.

Ljuben Mutafchiev (1995)

Aequationes mathematicae

Locally restricted compositions. I. Restricted adjacent differences.

Bender, Edward A., Canfield, E. Rodney (2005)

The Electronic Journal of Combinatorics [electronic only]

Locally restricted compositions. II: General restrictions and infinite matrices.

Bender, Edward A., Canfield, E.Rodney (2009)

The Electronic Journal of Combinatorics [electronic only]

Locally restricted compositions. III: Adjacent-part periodic inequalities.

Bender, Edward A., Canfield, E.Rodney (2010)

The Electronic Journal of Combinatorics [electronic only]

Longest alternating subsequences in pattern-restricted permutations.

Firro, Ghassan, Mansour, Toufik, Wilson, Mark C. (2007)

The Electronic Journal of Combinatorics [electronic only]

Longest increasing subsequences in pattern-restricted permutations.

Deutsch, Emeric, Hildebrand, A.J., Wilf, Herbert S. (2003)

The Electronic Journal of Combinatorics [electronic only]

Meet and join within the lattice of set partitions.

Canfield, Rodney E. (2001)

The Electronic Journal of Combinatorics [electronic only]

Multivariate asymptotics for products of large powers with applications to Lagrange inversion.

Bender, Edward A., Richmond, L.Bruce (1999)

The Electronic Journal of Combinatorics [electronic only]

Odd cutsets and the hard-core model on $ℤ^{d}$

Ron Peled, Wojciech Samotij (2014)

Annales de l'I.H.P. Probabilités et statistiques

We consider the hard-core lattice gas model on $ℤ^{d}$ and investigate its phase structure in high dimensions. We prove that when the intensity parameter exceeds $C d^{- 1 / 3} {(log d)}^{2}$ , the model exhibits multiple hard-core measures, thus improving the previous bound of $C d^{- 1 / 4} {(log d)}^{3 / 4}$ given by Galvin and Kahn. At the heart of our approach lies the study of a certain class of edge cutsets in $ℤ^{d}$ , 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.

Bóna, Miklós (2006)

The Electronic Journal of Combinatorics [electronic only]

On an integer sequence related to a product of trigonometric functions, and its combinatorial relevance.

Andrica, Dorin, Tomescu, Ioan (2002)

Journal of Integer Sequences [electronic only]

On averages of randomized class functions on the symmetric groups and their asymptotics

Paul-Olivier Dehaye, Dirk Zeindler (2013)

Annales de l’institut Fourier

The second author had previously obtained explicit generating functions for moments of characteristic polynomials of permutation matrices ( $n$ 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...

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