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A335725 The number of sigma matrices on the set of all endofunctions as a function of domain size n. 0

%I

%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

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