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- David Callan
- 2005

The monic sequence that shifts left under convolution with itself is the Catalan numbers with 130+ combinatorial interpretations. Here we establish a combinatorial interpretation for the monicâ€¦ (More)

- David Callan
- 2006

Sierpinski's triangle is a fractal and the Prouhet-Thue-Morse word is suÃ†ciently chaotic to avoid cubes. Here we observe that there is at least a tenuous connection between them: the Sierpinskiâ€¦ (More)

- Jody McNally, David Callan, Nicholas Matthew Andronicos, Nathan J. Bott, Peter W. Hunt
- Veterinary parasitology
- 2013

The presence of gastrointestinal nematode eggs in faecal samples is diagnostic of infection by these parasites. However, this technique cannot be used to distinguish between species of importance.â€¦ (More)

- David Callan
- 2009

We survey combinatorial interpretations of some dozen identities for the double factorial such as, for instance, (2nâˆ’ 2)!! + âˆ‘n k=2 (2nâˆ’1)!!(2kâˆ’4)!! (2kâˆ’1)!! = (2n âˆ’ 1)!!.

- David Callan
- 2004

A stabilized-interval-free (SIF) permutation on [n] = {1, 2, ..., n} is one that does not stabilize any proper subinterval of [n]. By presenting a decomposition of an arbitrary permutation into aâ€¦ (More)

- David Callan
- Eur. J. Comb.
- 2010

Martin Klazar computed the total weight of ordered trees under 12 different notions of weight. The last and perhaps most interesting of these weights, w12, led to a recurrence relation and anâ€¦ (More)

Nicholas Pippenger and Kristin Schleich have recently given a combinatorial interpretation for the second-order super-Catalan numbers (un)n 0 = (3; 2; 3; 6; 14; 36; :::): they count \aligned cubicâ€¦ (More)

- David Callan
- 2007

There are at least three di erent bijections in the literature from Dyck paths to 321-avoiding permutations, due to Billey-Jockusch-Stanley, Krattenthaler, and Mansour-Deng-Du. How di erent are they?â€¦ (More)

- David Callan, Len Smiley
- 2005

We consider noncrossing partitions of [n], taken up to rotation and/or reflection. Taken up to rotation, we exhibit a bijection to bicolored plane trees on n edges, and consider its implications.â€¦ (More)

- David Callan
- Discrete Mathematics & Theoretical Computerâ€¦
- 2008

We show that a determinant of Stirling cycle numbers counts unlabeled acyclic single-source automata. The proof involves a bijection from these automata to certain marked lattice paths and aâ€¦ (More)