The Fibonacci number of a grid graph and a new class of integer sequences.
The fraction of subspaces of with a specified number of minimal weight vectors is asymptotically Poisson.
The generating function of ternary trees and continued fractions.
The half-perimeter generating function of gated and wicketed Ferrers diagrams.
The hyperharmonic numbers and the phratry of the coupon collector. (Les nombres hyperharmoniques et la fratrie du collectionneur de vignettes.)
The initial involution patterns of permutations.
The insertion encoding of permutations.
The integer sequence A002620 and upper antagonistic functions.
The Josephus problem
We give explicit non-recursive formulas to compute the Josephus-numbers and and explicit upper and lower bounds for (where ) which differ by (for the bounds are even better). Furthermore we present a new fast algorithm to calculate which is based upon the mentioned bounds.
The kernel method: a collection of examples.
The Lagrange inversion formula and divisibility properties.
The major counting of nonintersecting lattice paths and generating functions for tableaux. (Summary).
The maximum number of perfect matchings in graphs with a given degree sequence.
The Nekrasov-Okounkov hook length formula: refinement, elementary proof, extension and applications
The paper is devoted to the derivation of the expansion formula for the powers of the Euler Product in terms of partition hook lengths, discovered by Nekrasov and Okounkov in their study of the Seiberg-Witten Theory. We provide a refinement based on a new property of -cores, and give an elementary proof by using the Macdonald identities. We also obtain an extension by adding two more parameters, which appears to be a discrete interpolation between the Macdonald identities and the generating function...
The number of 1-factors in some polyhexes.
The Number Of Antichains Of Finite Power Sets
The number of antichains of finite power sets.
The number of certain -combinations of an -set.
The number of elements in the mutation class of a quiver of type .
The number of indecomposable Schur rings over a cyclic 2-group.