Let $T$ be a non-trivial tournament. An arc is emph{$t$-pancyclic} in $T$, if it is contained in a cycle of length $ell$ for every $tleq ell leq |V(T)|$. Let $p^t(T)$ denote the number of $t$-pancyclic arcs in $T$ and $h^t(T)$ the maximum number of $t$-pancyclic arcs contained in the same Hamiltonian cycle of $T$. Moon ({em J. Combin. Inform. System Sci.}, {bf 19} (1994), 207-214) showed that $...

A bstract We generate a class of string backgrounds by sequence TsT transformations the NS1-NS5 system that we argue are holographically dual to states in single-trace $$ T\overline{T} T ¯ + J\overline{T} J T\overline{J} -deformed CFT 2 . The new incl...