Magic -cubes form a free monoid.
Matchings in complete bipartite graphs and the -Lah numbers
We give a graph theoretic interpretation of -Lah numbers, namely, we show that the -Lah number counting the number of -partitions of an -element set into ordered blocks is just equal to the number of matchings consisting of edges in the complete bipartite graph with partite sets of cardinality and (, ). We present five independent proofs including a direct, bijective one. Finally, we close our work with a similar result for -Stirling numbers of the second kind.
Mellin's Formula and Some Combinatorial Identities.
Mesh patterns and the expansion of permutation statistics as sums of permutation patterns.
Meta-Fibonacci sequences, binary trees and extremal compact codes.
Monomer-dimer tatami tilings of rectangular regions.
Motzkin numbers, central trinomial coefficients and hybrid polynomials.