19 citations · 95 across the 27 of their papers we have counts for
4 papers · 2 filters
A bijection on Dyck paths and its cycle structure
David Callan
The known bijections on Dyck paths are either involutions or have notoriously intractable cycle structure. Here we present a size-preserving bijection on Dyck paths whose cycle str…
Sierpinski's triangle and the Prouhet-Thue-Morse word
David Callan
Sierpinski's triangle is a fractal and the Prouhet-Thue-Morse word is sufficiently chaotic to avoid cubes. Here we observe that there is at least a tenuous connection between them:…
Permutations avoiding a nonconsecutive instance of a 2- or 3-letter pattern
David Callan
We count permutations avoiding a nonconsecutive instance of a two- or three-letter pattern, that is, the pattern may occur but only as consecutive entries in the permutation. Two-l…
A Combinatorial Interpretation of j/n {kn}\choose{n+j}
David Callan
The identity j/n {kn}\choose{n+j} =(k-1) {kn-1}\choose{n+j-1}- {kn-1}\choose{n+j} shows that j/n {kn}\choose{n+j} is always an integer. Here we give a combinatorial interpretation…