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Full-Text Articles in Physical Sciences and Mathematics
Permutation Invariant Lattices, Lenny Fukshansky, Stephan Ramon Garcia, Xun Sun
Permutation Invariant Lattices, Lenny Fukshansky, Stephan Ramon Garcia, Xun Sun
CMC Faculty Publications and Research
We say that a Euclidean lattice in Rn is permutation invariant if its automorphism group has non-trivial intersection with the symmetric group Sn, i.e., if the lattice is closed under the action of some non-identity elements of Sn. Given a fixed element τ ∈ Sn, we study properties of the set of all lattices closed under the action of τ: we call such lattices τ-invariant. These lattices naturally generalize cyclic lattices introduced by Micciancio in [8, 9], which we previously studied in [1]. Continuing our investigation, we discuss some basic properties of permutation invariant lattices, in particular proving that the …
Permutation Invariant Lattices, Lenny Fukshansky, Stephan Ramon Garcia, Xun Sun
Permutation Invariant Lattices, Lenny Fukshansky, Stephan Ramon Garcia, Xun Sun
Pomona Faculty Publications and Research
We say that a Euclidean lattice in Rn is permutation invariant if its automorphism group has non-trivial intersection with the symmetric group Sn, i.e., if the lattice is closed under the action of some non-identity elements of Sn. Given a fixed element T E Sn, we study properties of the set of all lattices closed under the action of T: we call such lattices T-invariant. These lattices naturally generalize cyclic lattices introduced by Micciancio in [7,8], which we previously studied in [1]. Continuing our investigation, we discuss some basic properties of …