منابع مشابه
Generalized Higher Order Spt-functions
We give a new generalization of the spt-function of G.E. Andrews, namely Sptj(n), and give its combinatorial interpretation in terms of successive lower-Durfee squares. We then generalize the higher order spt-function sptk(n), due to F.G. Garvan, to jsptk(n), thus providing a two-fold generalization of spt(n), and give its combinatorial interpretation.
متن کاملHigher Order Spt-functions
Andrews’ spt-function can be written as the difference between the second symmetrized crank and rank moment functions. Using the machinery of Bailey pairs a combinatorial interpretation is given for the difference between higher order symmetrized crank and rank moment functions. This implies an inequality between crank and rank moments that was only known previously for sufficiently large n and...
متن کاملSoft asymptotics for generalized spt-functions
We derive a leading order asymptotic for the difference between the second moments of Garvan’s generalized rank statistics. The approach uses Dixit and Yee’s combinatorial interpretation of the difference and soft probabilistic techniques to deal with random partitions.
متن کاملSolving Higher Order Functions
In this paper we extend the class of energy functions for which the optimal α-expansion and αβswap moves can be computed in polynomial time. Specifically, we introduce a novel family of higher order clique potentials and show that the expansion and swap moves for any energy function composed of these potentials can be found by minimizing a submodular function. We also show that for a subset of ...
متن کاملTesting Higher Order Functions
Automatic testing of first order functions works fine. Testing higher order functions automatically is more troublesome, it is harder to generate the functions needed as argument automatically, and these generated functions cannot be shown when a counterexample is found. Nevertheless, higher order functions can contain errors and hence need to be tested. In this paper we present effective and e...
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ژورنال
عنوان ژورنال: The Ramanujan Journal
سال: 2012
ISSN: 1382-4090,1572-9303
DOI: 10.1007/s11139-012-9434-2