An orthomorphism, π, of a group, (G, +), is a permutation of G with the property that the map x → -x + π(x) is also a permutation. In this paper, we consider orthomorphisms of the additive group of binary n-tuples, Zn2. We use known orthomorphism preserving functions to prove a uniformity in the cycle types of orthomorphisms that extend certain partial orthomorphisms, and prove that extensions of particular sizes of partial orthomorphisms exist. Further, in studying the action of conjugating orthomorphisms by automorphisms, we find several symmetries within the orbits and stabilizers of this action, and other orthomorphism-preserving functions. In addition, we prove a lower bound on the number of orthomorphisms of Zn2 using the equivalence ...
This thesis deals with two related combinatorial topics, namely cyclotomic orthomorphisms and diagon...
Let B-p be the Latin square given by the addition table for the integers modulo an odd prime p (i.e....
In this paper we examine algebraic properties of quasigroups produced by diagonal method from orthom...
A partial orthomorphism of a group GG (with additive notation) is an injection π:S→G for some S⊆G su...
This book is about orthomorphisms and complete mappings of groups, and related constructions of orth...
AbstractBlock substitutions, or bijective mappings of n-bit binary n-tuples, are widely used in cryp...
AbstractBlock substitutions, or bijective mappings of n-bit binary n-tuples, are widely used in cryp...
AbstractA permutation σ on F2n is an orthomorphism iff the mapping x↦x+σ(x) is also a permutation on...
We fix a Boolean subalgebra B of an orthomodular poset P and study the mappings s: P → [0, 1] which ...
We fix a Boolean subalgebra B of an orthomodular poset P and study the mappings s:P → [0,1] which re...
We fix a Boolean subalgebra B of an orthomodular poset P and study the mappings s: P → [0, 1] which ...
AbstractWe prove that if m>3 is odd and not divisible by 9 then we can construct a pair of orthogona...
AbstractFor n 1, 5 (mod 6) it is shown that the dihedral group of order 4n admits a pair of orthog...
This thesis deals with two related combinatorial topics, namely cyclotomic orthomorphisms and diagon...
We study orthoalgebra morphisms, we show how orthoalgebra monomorphisms and epimorphisms ought to be...
This thesis deals with two related combinatorial topics, namely cyclotomic orthomorphisms and diagon...
Let B-p be the Latin square given by the addition table for the integers modulo an odd prime p (i.e....
In this paper we examine algebraic properties of quasigroups produced by diagonal method from orthom...
A partial orthomorphism of a group GG (with additive notation) is an injection π:S→G for some S⊆G su...
This book is about orthomorphisms and complete mappings of groups, and related constructions of orth...
AbstractBlock substitutions, or bijective mappings of n-bit binary n-tuples, are widely used in cryp...
AbstractBlock substitutions, or bijective mappings of n-bit binary n-tuples, are widely used in cryp...
AbstractA permutation σ on F2n is an orthomorphism iff the mapping x↦x+σ(x) is also a permutation on...
We fix a Boolean subalgebra B of an orthomodular poset P and study the mappings s: P → [0, 1] which ...
We fix a Boolean subalgebra B of an orthomodular poset P and study the mappings s:P → [0,1] which re...
We fix a Boolean subalgebra B of an orthomodular poset P and study the mappings s: P → [0, 1] which ...
AbstractWe prove that if m>3 is odd and not divisible by 9 then we can construct a pair of orthogona...
AbstractFor n 1, 5 (mod 6) it is shown that the dihedral group of order 4n admits a pair of orthog...
This thesis deals with two related combinatorial topics, namely cyclotomic orthomorphisms and diagon...
We study orthoalgebra morphisms, we show how orthoalgebra monomorphisms and epimorphisms ought to be...
This thesis deals with two related combinatorial topics, namely cyclotomic orthomorphisms and diagon...
Let B-p be the Latin square given by the addition table for the integers modulo an odd prime p (i.e....
In this paper we examine algebraic properties of quasigroups produced by diagonal method from orthom...