Lettre à M. Bourget sur un article des Nouvelles annales
Limit shapes of Gibbs distributions on the set of integer partitions : the expansive case
We find limit shapes for a family of multiplicative measures on the set of partitions, induced by exponential generating functions with expansive parameters, ak∼Ckp−1, k→∞, p>0, where C is a positive constant. The measures considered are associated with the generalized Maxwell–Boltzmann models in statistical mechanics, reversible coagulation–fragmentation processes and combinatorial structures, known as assemblies. We prove a central limit theorem for fluctuations of a properly scaled partition...
Lindelöf representations and (non-)holonomic sequences.
Linear and ring arrangements
Linear complementarity problem and extremal hyperplanes
Linear differential equations and multiple zeta values. I. Zeta(2)
Certain generating fuctions for multiple zeta values are expressed as values at some point of solutions of linear meromorphic differential equations. We apply asymptotic expansion methods (like the WKB method and the Stokes operators) to solutions of these equations. In this way we give a new proof of the Euler formula ζ(2) = π²/6. In further papers we plan to apply this method to study some third order hypergeometric equation related to ζ(3).
Linear recurrent sequences and powers of a square matrix.
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.
Log-balanced combinatorial sequences.
Longest alternating subsequences in pattern-restricted permutations.
Longest increasing subsequences in pattern-restricted permutations.
Longest increasing subsequences of random colored permutations.
Lyndon words and transition matrices between elementary, homogeneous and monomial symmetric functions.
-rank differences for partitions without repeated odd parts
We prove formulas for the generating functions for -rank differences for partitions without repeated odd parts. These formulas are in terms of modular forms and generalized Lambert series.
-partition boards and poly-Stirling numbers.
M₂-rank differences for overpartitions
MacMahon's partition analysis. IV: Hypergeometric multisums.