Trees and meta-Fibonacci sequences.
Truncating binomial series with symbolic summation.
Two analogues of a classical sequence.
Two coefficients of the Dyson product.
Two combinatorial problems in group theory
Two congruences involving 4-cores.
Two finite forms of Watson's quintuple product identity and matrix inversion.
Two game-set inequalities.
Two involutions for signed excedance numbers.
Two new criteria for comparison in the Bruhat order.
Two sided Sand Piles Model and unimodal sequences
We introduce natural generalizations of two well-known dynamical systems, the Sand Piles Model and the Brylawski's model. We describe their order structure, their reachable configuration's characterization, their fixed points and their maximal and minimal length's chains. Finally, we present an induced model generating the set of unimodal sequences which amongst other corollaries, implies that this set is equipped with a lattice structure.
Two statistics linking Dyck paths and non-crossing partitions.
Two very short proofs of combinatorial identity.
Two-stage allocations and the double -function.