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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
- 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
- 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)

- 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
- 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)

- David Callan
- 2004

Nicholas Pippenger and Kristin Schleich have recently given a combinatorial interpretation for the second-order super-Catalan numbers (un)nâ‰¥0 = (3, 2, 3, 6, 14, 36, ...): they count â€œaligned cubicâ€¦ (More)

- David Callan, Len Smiley
- 2005

We consider noncrossing partitions of [n] under the action of (i) the reflection group (of order 2), (ii) the rotation group (cyclic of order n) and (iii) the rotation/reflection group (dihedral ofâ€¦ (More)

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: the Sierpinskiâ€¦ (More)

- Marsha McGhee, Scott J Stern, David Callan, Kristopher Shewmake, Terry Smith
- Head & neck
- 1997

BACKGROUND
Osseointegrated implants allow patients with oromandibular defects to obtain complete or partial dentition via implant-assisted or implant-borne prostheses. Implants restore masticatoryâ€¦ (More)

- David Callan
- 2009

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