Franklin's argument proves an identity of Zagier.
Frankl’s conjecture for large semimodular and planar semimodular lattices
A lattice is said to satisfy (the lattice theoretic version of) Frankl’s conjecture if there is a join-irreducible element such that at most half of the elements of satisfy . Frankl’s conjecture, also called as union-closed sets conjecture, is well-known in combinatorics, and it is equivalent to the statement that every finite lattice satisfies Frankl’s conjecture. Let denote the number of nonzero join-irreducible elements of . It is well-known that consists of at most elements....
Frobenius numbers by lattice point enumeration.
Frobenius symbols for partitions and degrees of spin characters.
From -Motzkin paths to Schröder paths.
From a Ramsey-type theorem to indepedence
From double Hecke algebra to analysis.
From paths to stars.
From recursions to asymptotics: On Szekeres' formula for the number of partitions.
Fuchsian differential equation for the perimeter generating function of three-choice polygons.
Full subsets of .
Fully degenerate poly-Bernoulli numbers and polynomials
In this paper, we introduce the new fully degenerate poly-Bernoulli numbers and polynomials and inverstigate some properties of these polynomials and numbers. From our properties, we derive some identities for the fully degenerate poly-Bernoulli numbers and polynomials.