Integer sequences related to compositions without 2's.
Inversion statistics of MacMohan and of Goulden and Jackson. (Über die Inversionsstatistiken von MacMahon und Goulden-Jackson.)
Irreducible symmetric group characters of rectangular shape.
-complementing subsets of nonnegative integers.
Kombinatorik mit dem Computer: Klassifikationen und damit verwandte Figuren.
Kombinatorik mit dem Computer: Partitionen und Frankaturen.
La théorie classique et moderne des fonctions symétriques
Limit shapes of Gibbs distributions on the set of integer partitions : the expansive case
We find limit shapes for a family of multiplicative measures on the set of partitions, induced by exponential generating functions with expansive parameters, ak∼Ckp−1, k→∞, p>0, where C is a positive constant. The measures considered are associated with the generalized Maxwell–Boltzmann models in statistical mechanics, reversible coagulation–fragmentation processes and combinatorial structures, known as assemblies. We prove a central limit theorem for fluctuations of a properly scaled partition...
-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.
M₂-rank differences for overpartitions
MacMahon's partition analysis. IV: Hypergeometric multisums.
MacMahon's partition analysis XI: Broken diamonds and modular forms
Matrix compositions.
Maximal projective degrees for strict partitions.
Maximum product over partitions into distinct parts.
Methode der periodischen Zahlen und Doppelpartition.
Mince zajímají nejen numismatiky
V článku představíme dva druhy úloh týkajících se platby mincemi, které souvisejí s optimalitou počtu použitých mincí. V případě problému platby (říká se také rozměňování — anglicky change making problem), tj. skládání částky z mincí bez možnosti vracení, jsou úlohy spojené s optimalitou dobře prozkoumané. Analogické úlohy zformulujeme pro směnu, tj. skládání částky z mincí s možností vracení. Zde zůstává naopak řada problémů otevřená.
Minimal -complete partitions.
Mock modular forms and singular combinatorial series
A celebrated result of Bringmann and Ono shows that the combinatorial rank generating function exhibits automorphic properties after being completed by the addition of a non-holomorphic integral. Since then, automorphic properties of various related combinatorial families have been studied. Here, extending work of Andrews and Bringmann, we study general infinite families of combinatorial q-series pertaining to k-marked Durfee symbols, in which we allow additional singularities. We show that these...
Monadic epimorphisms and applications