We characterise the intermediate logics which admit a cut-free hypersequent calculus of the form HLJ+ R, where HLJ is the hypersequent counterpart of the sequent calculus LJ for propositional intuitionistic logic, and R is a set of so-called structural hypersequent rules, i.e., rules not involving any logical connectives. The characterisation of this class of intermediate logics is presented bo...

We establish an improved lower bound of 10.271 for the exponential growth rate of the class of permutations avoiding the pattern 1324, and an improved upper bound of 13.5. These results depend on a new exact structural characterisation of 1324-avoiders as a subclass of an infinite staircase grid class, together with precise asymptotics of a small domino subclass whose enumeration we relate to W...

We establish an improved lower bound of 10.271 for the exponential growth rate of the class of permutations avoiding the pattern 1324, and an improved upper bound of 13.5. These results depend on a new exact structural characterisation of 1324-avoiders as a subclass of an infinite staircase grid class, together with precise asymptotics of a small “domino” subclass whose enumeration is related t...