-rank differences for partitions without repeated odd parts
We prove formulas for the generating functions for -rank differences for partitions without repeated odd parts. These formulas are in terms of modular forms and generalized Lambert series.
-partition boards and poly-Stirling numbers.
M₂-rank differences for overpartitions
MacMahon's partition analysis. IV: Hypergeometric multisums.
MacMahon's partition analysis XI: Broken diamonds and modular forms
MacMahon's theorem for a set of permutations with given descent indices and right-maximal records.
MacMahon-type identities for signed even permutations.
Magic -cubes form a free monoid.
Magic squares, rook polynomials and permutations.
Mahler's expansion and Boolean functions.
Many Triangulated Spheres.
Mappings of Acyclic and Parking Functions.
Mario Ouellette's arborescent decomposition for species of structures. (Décomposition arborescente de Mario Ouellette pour les espèces de structures.)
Matchings and partial patterns.
Matchings avoiding partial patterns.
Matchings avoiding partial patterns and lattice paths.
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.
Matchings in infinite graphs
Mathematics of Ghaly's machine.
Matrix compositions.