منابع مشابه
Counting k-Marked Durfee Symbols
An alternative characterization of k-marked Durfee symbols defined by Andrews is given. Some identities involving generating functions of k-marked Durfee symbols are proven combinatorially by considering the symbols not individually, but in equivalence classes. Also, a related binomial coefficient identity is obtained in the course. A partition λ of a positive integer n is a nonincreasing seque...
متن کاملThe combinatorics of k - marked Durfee symbols Kathy
Andrews recently introduced k-marked Durfee symbols which are connected to moments of Dyson’s rank. By these connections, Andrews deduced their generating functions and some combinatorial properties and left their purely combinatorial proofs as open problems. The primary goal of this article is to provide combinatorial proofs in answer to Andrews’ request. We obtain a relation between k-marked ...
متن کاملInequalities for full rank differences of 2-marked Durfee symbols
In this paper, we obtain infinitely many non-trivial identities and inequalities between full rank differences for 2-marked Durfee symbols, a generalization of partitions introduced by Andrews. A certain strict inequality, which almost always holds, shows that identities for Dyson’s rank, similar to those proven by Atkin and Swinnerton-Dyer, are quite rare. By showing an analogous strict inequa...
متن کاملAndrews’ 2-marked Durfee Symbols and Weak Maass Forms
The modularity of the partition generating function has many important consequences, for example asymptotics and congruences for p(n). In a series of papers the author and Ono connected the rank, a partition statistic introduced by Dyson, to weak Maass forms, a new class of functions which are related to modular forms. Here we place the 2-marked Durfee symbols introduced by Andrews [1] into the...
متن کاملWeighted Model Counting With Function Symbols
Probabilistic relational languages lift the syntax of relational logic for the specification of large-scale probabilistic graphical models, often admitting concise descriptions for interacting random variables over classes, hierarchies and constraints. The emergence of weighted model counting as an effective and general approach to probabilistic inference has further allowed practitioners to re...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: The Electronic Journal of Combinatorics
سال: 2010
ISSN: 1077-8926
DOI: 10.37236/528