SOME OBSERVATIONS AND SPECULATIONS ON PARTITIONS INTO d-TH POWERS
نویسندگان
چکیده
منابع مشابه
Partitions of an Integer into Powers
In this paper, we use a simple discrete dynamical model to study partitions of integers into powers of another integer. We extend and generalize some known results about their enumeration and counting, and we give new structural results. In particular, we show that the set of these partitions can be ordered in a natural way which gives the distributive lattice structure to this set. We also giv...
متن کاملSome Observations on Dyson's New Symmetries of Partitions
We utilize Dyson’s concept of the adjoint of a partition to derive an infinite family of new polynomial analogues of Euler’s Pentagonal Number Theorem. We streamline Dyson’s bijection relating partitions with crank ≤ k and those with k in the Rank-Set of partitions. Also, we extend Dyson’s adjoint of a partition to MacMahon’s “modular” partitions with modulus 2. This way we find a new combinato...
متن کاملSome formulae for partitions into squares
We consider the problem of determining the number of partitions of a number into a fixed number of squares. This problem is distinct from, but not unrelated to, the corresponding classical problem of determining the number of representations of a number as the sum of a fixed number of squares. Whereas the classical problem has received an enormous amount of attention over the years, see Dickson...
متن کاملElectron microscopic observations and speculations on Australia antigen JUNE D . ALMEIDA
THE correlation between the Australia antigen and serum hepatitis is now so good (Le Bouvier & McCollum, 1970) that a study of the one is automatically a study of the other. This paper deals with one aspect of these studies, the morphology as seen by the electron microscope technique of negative staining. It will consider the practical use to which this morphological information can be put and ...
متن کاملStrange Quark stars: Observations & Speculations
Two kinds of difficulties have challenged the physics community for many years: (1) knowing nature’s building blocks (particle physics) and (2) understanding interacting many-body systems (many-body physics). Both of them exist in the research of quark matter and compact stars. This paper addresses the possibility that quark clustering, rather than a color super-conducting state, could occur in...
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: Bulletin of the Australian Mathematical Society
سال: 2021
ISSN: 0004-9727,1755-1633
DOI: 10.1017/s0004972721000034