19 citations · 87 across the 21 of their papers we have counts for
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A combinatorial interpretation for a super-Catalan recurrence
David Callan
Nicholas Pippenger and Kristin Schleich have recently given a combinatorial interpretation for the second-order super-Catalan numbers (u_{n})_{n>=0}=(3,2,3,6,14,36,...): they count…
Some bijections for restricted Motzkin paths
David Callan
We give several bijections among restricted Motzkin paths, explaining why various parameters on these paths are equidistributed. For example, the number of doublerise-free Motzkin…
Two Bijections for Dyck Path Parameters
David Callan
Here we give two bijections, one to show that the number of UUU-free Dyck n-paths is the Motzkin number M_n, the other to obtain the (known) distributions of the parameters "number…
A combinatorial proof of Sun's "curious" identity
David Callan
A binomial coefficient identity due to Zhi-Wei Sun is the subject of half a dozen recent papers that prove it by various analytic techniques and establish a generalization. Here we…