The exact asymptotic of the time to collision.
The fundamental group of a locally finite graph with ends-a hyperfinite approach
The end compactification |Γ| of a locally finite graph Γis the union of the graph and its ends, endowed with a suitable topology. We show that π₁(|Γ|) embeds into a nonstandard free group with hyperfinitely many generators, i.e. an ultraproduct of finitely generated free groups, and that the embedding we construct factors through an embedding into an inverse limit of free groups. We also show how to recover the standard description of π₁(|Γ|) given by Diestel and Sprüssel (2011). Finally, we give...
The fundamental group of balanced simplicial complexes and posets.
The Garnir relations for Weyl groups of type .
The generalized weighted probability measure on the symmetric group and the asymptotic behavior of the cycles
The goal of this paper is to analyse the asymptotic behaviour of the cycle process and the total number of cycles of weighted and generalized weighted random permutations which are relevant models in physics and which extend the Ewens measure. We combine tools from combinatorics and complex analysis (e.g. singularity analysis of generating functions) to prove that under some analytic conditions (on relevant generating functions) the cycle process converges to a vector of independent Poisson variables...
The hive model and the factorisation of Kostka coefficients.
The hive model and the polynomial nature of stretched Littlewood-Richardson coefficients.
The hook fusion procedure.
The hyperharmonic numbers and the phratry of the coupon collector. (Les nombres hyperharmoniques et la fratrie du collectionneur de vignettes.)
The hyperplanes of .
The integer sequence A002620 and upper antagonistic functions.
The Littlewood-Richardson rule - the cornerstone for computing group properties
The major counting of nonintersecting lattice paths and generating functions for tableaux. (Summary).
The matching polynomial of a distance-regular graph.
The maximum distinguishing number of a group.
The maximum size of a partial spread in is .
The multiplicities of a dual-thin -polynomial association scheme.
The nonexistence of regular near octagons with parameters .
The number of complete exceptional sequences for a Dynkin algebra
The Dynkin algebras are the hereditary artin algebras of finite representation type. The paper determines the number of complete exceptional sequences for any Dynkin algebra. Since the complete exceptional sequences for a Dynkin algebra of Dynkin type Δ correspond bijectively to the maximal chains in the lattice of non-crossing partitions of type Δ, the calculations presented here may also be considered as a categorification of the corresponding result for non-crossing partitions.
The number of indecomposable Schur rings over a cyclic 2-group.