The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.



Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 56th year, we are closing in on 350,000 sequences, and we’ve crossed 9,700 citations (which often say “discovered thanks to the OEIS”).

(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A335725 The number of sigma matrices on the set of all endofunctions as a function of domain size n. 0


%S 1,2,5,13,35,93,260

%N The number of sigma matrices on the set of all endofunctions as a function of domain size n.

%C The number of unique sigma matrices of endofunctions as a function of n where n is the size of the finite domain. The sigma matrix is an n X n preimage data structure in which an arbitrary entry is given by sigma[i,j] = abs(f(x_{i})^{-j}). In other words, given an endofunction on X, the sigma matrix captures the size of the j-back inverse applied to the i-th domain element of X.

%D Fournier-Eaton, Bradford M., "A Theory of Preimage Complexity: Data-structures, Complexity Measures and Applications to Endofunctions and Associated Digraphs" (2020). University of New Orleans Theses and Dissertations. 2794.

%e A two element domain corresponds to n=2. There are 2^2=4 endofunctions on two elements. However the only unique sigma matrices correspond to S1 = [[2,2],[0,0]] and S2 = [[1,1],[1,1]], and thus sigma(2)=2. See the referenced dissertation at the associated link for a full exposition including examples, definitions and theory.

%K nonn,hard,more

%O 1,2

%A _Bradford M. Fournier-Eaton_, Jun 19 2020

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified December 2 05:01 EST 2021. Contains 349437 sequences. (Running on oeis4.)