More Monotonicity Theorems for Partitions
نویسندگان
چکیده
Consider the collection of all integer partitions, whose part sizes lie in a given set. Such a set is called monotone if the generating function has weakly increasing coefficients. The monotone subsets are classified, assuming an open conjecture.
منابع مشابه
The Seidel, Stern, Stolz and Van Vleck Theorems on continued fractions
The usual proofs of these three classical theorems are based on the sequences bn, An and Bn, where Zn = An/Bn, and the three-term recurrence relations for An and Bn. Our aim is to unify and generalise these results by giving new, geometric, proofs (apart from the elementary monotonicity statement, and subsequent convergence, in Theorem 1.1). First, however, we restate these three results (again...
متن کاملNew Weighted Rogers-ramanujan Partition Theorems and Their Implications
This paper has a two-fold purpose. First, by considering a reformulation of a deep theorem of Göllnitz, we obtain a new weighted partition identity involving the Rogers-Ramanujan partitions, namely, partitions into parts differing by at least two. Consequences of this include Jacobi’s celebrated triple product identity for theta functions, Sylvester’s famous refinement of Euler’s theorem, as we...
متن کاملMonotonicity Theorems for Laplace Beltrami Operator on Riemannian Manifolds
Abstract. For free boundary problems on Euclidean spaces, the monotonicity formulas of Alt-Caffarelli-Friedman and Caffarelli-Jerison-Kenig are cornerstones for the regularity theory as well as the existence theory. In this article we establish the analogs of these results for the LaplaceBeltrami operator on Riemannian manifolds. As an application we show that our monotonicity theorems can be e...
متن کاملLimit Theorems for the Number of Summands in Integer Partitions
Central and local limit theorems are derived for the number of distinct summands in integer partitions, with or without repetitions, under a general scheme essentially due to Meinardus. The local limit theorems are of the form of Cramér-type large deviations and are proved by Mellin transform and the two-dimensional saddle-point method. Applications of these results include partitions into posi...
متن کاملLegendre theorems for subclasses of overpartitions
A. M. Legendre noted that Euler’s pentagonal number theorem implies that the number of partitions of n into an even number of distinct parts almost always equals the number of partitions of n into an odd number of distinct parts (the exceptions occur when n is a pentagonal number). Subsequently other classes of partitions, including overpartitions, have yielded related Legendre theorems. In thi...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید
ثبت ناماگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید
ورودعنوان ژورنال:
- Experimental Mathematics
دوره 3 شماره
صفحات -
تاریخ انتشار 1994