Partitions with Rounded Occurrences and Attached Parts

Partitions and Overpartitions with Attached Parts

We show how to interpret a certain q-series as a generating function for overpartitions with attached parts. A number of families of partition theorems follow as corollaries.

Overpartition Theorems of the Rogers-ramanujan Type

We give one-parameter overpartition-theoretic analogues of two classical families of partition identities: Andrews’ combinatorial generalization of the Gollnitz-Gordon identities and a theorem of Andrews and Santos on partitions with attached odd parts. We also discuss geometric counterparts arising from multiple q-series identities. These involve representations of overpartitions in terms of g...

Enumeration of Partitions by Long Rises, Levels, and Descents

When the partitions of [n] = {1, 2, . . . , n} are identified with the restricted growth functions on [n], under a known bijection, certain enumeration problems for classical word statistics are formulated for set partitions. In this paper we undertake the enumeration of partitions of [n] with respect to the number of occurrences of rises, levels and descents, of arbitrary integral length not e...

Effect of Source Areas Anthropogenic Activities on Dust Storm Occurrences in the Western Parts of Iran

Term Partitions and Minimal Generalizations of Clauses

Term occurrences of any clause C are determined by their positions. The set of all term partitions defined on subsets of term occurrences of C form a partially ordered set. This poset is isomorphic to the set of all generalizations of C. The structure of this poset can be inferred from the term occurrences in C alone. We can apply these constructions in this poset in machine learning.