Injections, Surjections and More
نویسنده
چکیده
where is the natural logarithmic base [4]. In counting all injections, we treat extensions as distinct; for example, the function : {1 2}→ {1 2} with () = is not the same as the function : {1 2} → {1 2 3} with () = , nor is it the same as the function : {1 2 3}→ {1 2 3} with () = . Let denote the set of all surjections {1 } → {1 } where ≥ . An element of can be thought of as an ordered -tuple consisting of preimage blocks ( disjoint nonempty sets that cover symbols). We define 00 to possess one element (the empty tuple) for convenience; therefore [5, 6, 7]
منابع مشابه
On Efficient Bijections between Permutations and Functions
We explore efficient surjections and bijections between sets of functions and sets of permutations. These mappings are efficient in the sense that with only a few evaluations (polynomial in the size of inputs) of a black box representing either a function or permutation, we can evaluate the corresponding permutation or function for a particular input. It is not obvious that such efficient surje...
متن کاملRepresentations of Categories of G-maps
We study representations of wreath product analogues of categories of finite sets. This includes the category of finite sets and injections (studied by Church, Ellenberg, and Farb) and the opposite of the category of finite sets and surjections (studied by the authors in previous work). We prove noetherian properties for the injective version when the group in question is polycyclic-by-finite a...
متن کاملS-boxes and Round Functions with Controllable Linearity and Differential Uniformity
A b s t r a c t . In this contribution we consider the stability of linearity and differential uniformity of vector Boolean functions under certain constructions and modifications. These include compositions with affine surjections onto the input space and with aitlne surjections from the output space, inversions, adding coordinate functions, forming direct sums and restrictions to affine subsp...
متن کاملSome New Results on Binary Relations
It is well known that if a function from set A to set B has a right inverse then the function is a surjection and the right inverse is an injection. For finite sets, the number of functions, injections, and surjections can also be counted. Relations generalize functions: do similar results exist for relations? This paper proves several new results concerning binary relations. For finite sets, w...
متن کاملA Universal Property of the Monoidal 2-category of Cospans of Ordinals and Surjections
We prove that the monoidal 2-category of cospans of ordinals and surjections is the universal monoidal category with an object X with a semigroup and a cosemigroup structures, where the two structures satisfy a certain 2-dimensional separable algebra condition.
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
دوره شماره
صفحات -
تاریخ انتشار 2015