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n -T-quasigroup codes with one check symbol and their error detection capabilities

Gary L. Mullen, Viktor Alekseevich Shcherbakov (2004)

Commentationes Mathematicae Universitatis Carolinae

It is well known that there exist some types of the most frequent errors made by human operators during transmission of data which it is possible to detect using a code with one check symbol. We prove that there does not exist an n -T-code that can detect all single, adjacent transposition, jump transposition, twin, jump twin and phonetic errors over an alphabet that contains 0 and 1. Systems that detect all single, adjacent transposition, jump transposition, twin, jump twin errors and almost all...

Naive boundary strata and nilpotent orbits

Matt Kerr, Gregory Pearlstein (2014)

Annales de l’institut Fourier

We give a Hodge-theoretic parametrization of certain real Lie group orbits in the compact dual of a Mumford-Tate domain, and characterize the orbits which contain a naive limit Hodge filtration. A series of examples are worked out for the groups S U ( 2 , 1 ) , S p 4 , and G 2 .

Near heaps

Ian Hawthorn, Tim Stokes (2011)

Commentationes Mathematicae Universitatis Carolinae

On any involuted semigroup ( S , · , ' ) , define the ternary operation [ a b c ] : = a · b ' · c for all a , b , c ∈ S . The resulting ternary algebra ( S , [ ] ) satisfies the para-associativity law [ [ a b c ] d e ] = [ a [ d c b ] e ] = [ a b [ c d e ] ] , which defines the variety of semiheaps. Important subvarieties include generalised heaps, which arise from inverse semigroups, and heaps, which arise from groups. We consider the intermediate variety of near heaps, defined by the additional laws [ a a a ] = a and [ a a b ] = [ b a a ] . Every Clifford semigroup is a near heap when viewed as a semiheap, and we show that the Clifford semigroup...

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