Second-Degree Involutory Symbolic Substitutions

Involutory Differentially 4-Uniform Permutations from Known Constructions

Substitution box (S-box) is an important component of block ciphers for providing confusion into the cryptosystems. The functions used as S-boxes should have low differential uniformity, high nonlinearity and high algebraic degree. Due to the lack of knowledge on the existence of APN permutations over F22k , which have the lowest differential uniformity, when k > 3, they are often constructed f...

The Involutory Dimension of Involution Posets

The involutory dimension, if it exists, of an involution poset P := (P,≤,′ ) is the minimum cardinality of a family of linear extensions of ≤, involutory with respect to ′, whose intersection is the ordering ≤. We show that the involutory dimension of an involution poset exists iff any pair of isotropic elements are orthogonal. Some characterizations of the involutory dimension of such posets a...

Symbolic Significance of Yeats's "The Second Coming"

Subject Classiication (ams) 06f05 20m14

Two classes of linear involutory semigroups We construct two classes of involutory semigroups, which together with two already known generating rules yield n linear involutory semigroups of order n, where 2n = 2 n+2 ? 1 2 (n + 1)(n + 6) ; 2n+1 = 3 2 n+1 ? 1 2 (n 2 + 9n + 10) (1) for n 1. By the way, we extend the rule for the construction of linear archimedian involutory semigroups in L. Berg a...

Symbolic play connects to language through visual object recognition.

Object substitutions in play (e.g. using a box as a car) are strongly linked to language learning and their absence is a diagnostic marker of language delay. Classic accounts posit a symbolic function that underlies both words and object substitutions. Here we show that object substitutions depend on developmental changes in visual object recognition: 18- to 30-month old children (n = 63) subst...