The Lalanne–Kreweras involution is an on the set of Dyck paths which combinatorially exhibits symmetry number valleys and major index statistics. We define piecewise-linear birational extensions involution. Actually, we show that a special case more general operator, called rowvacuation, acts antichains any graded poset. Rowvacuation, like closely related studied rowmotion composition toggles. ...

In this paper, we propose a 128-bit block cipher ARIA which is an involution substitution and permutation encryption network(SPN). We use the same S-boxes as Rijndael to eliminate defects which are caused by a totally involution structure. In the diffusion layer of ARIA, a 16×16 binary matrix of the maximum branch number 8 is used to avoid some attacks well applied to the reduced round of Rijnd...

Jeffrey Adams, University of Maryland. The Chevalley Involution for Real Groups, with applications to the Fubini-Schur Indicator. The Chevalley involution of a complex group is unique up to conjugation, and takes any algebraic representation to its contragredient. The analogue over local fields is subtle. We prove that the Chevalley involution is defined over R, and with an appropriate conditio...

In this paper we study a generalization of the classical notions of solid codes and comma-free codes: involution solid codes (θ-solid) and involution join codes (θ-join). These notions are motivated by DNA strand design where Watson-Crick complementarity can be formalized as an antimorphic involution. We investigate closure properties of these codes, as well as necessary conditions for θ-solid ...

Introduction: Let C be a nonhyperelliptic smooth curve of genus π. An involution of C is an automorphism φ : C−→C such that φ = id. It induces a double cover γ : C−→C/φ = X , where X is a smooth curve of genus g. We say that C has an involution of genus g. By Hurwitz formula, we know that π ≥ 2g − 1. It is well know that a general smooth curve of genus π ≥ 3 has not nontrivial automorphisms. In...

Weakly hyperbolic involutions are introduced and a proof is given of the following local-global principle: a central simple algebra with involution of any kind is weakly hyperbolic if and only if its signature is zero for all orderings of the ground field. Also, the order of a weakly hyperbolic algebra with involution is a power of two, this being a direct consequence of a result of Scharlau. A...

In this article, we provide new methods to look for lightweight MDS matrices, and in particular involutory ones. By proving many new properties and equivalence classes for various MDS matrices constructions such as circulant, Hadamard, Cauchy and Hadamard-Cauchy, we exhibit new search algorithms that greatly reduce the search space and make lightweight MDS matrices of rather high dimension poss...

This paper aims to investigate properties of involution palindrome languages. Let θ be either a morphic or antimorphic involution. we show that if θ is an antimorphic involution, then the set of all θ-palindrome words is a proper subset of all skew θ-palindrome words. We give a characterization for that a word is skew θ-palindrome. That is, A word is skew θ-palindrome if and only if it is a pro...

An infinte word w avoids a pattern p with the involution θ if there is no substitution for the variables in p and no involution θ such that the resulting word is a factor of w. We investigate the avoidance of patterns with respect to the size of the alphabet. For example, it is shown that the pattern α θ (α)α can be avoided over three letters but not two letters, whereas it is well known that α...