19 citations · 52 across the 10 of their papers we have counts for
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On conjugates for set partitions and integer compositions
David Callan
There is a familiar conjugate for integer partitions: transpose the Ferrers diagram, and a conjugate for integer compositions: transpose a Ferrers-like diagram. Here we propose a c…
A combinatorial interpretation of the eigensequence for composition
David Callan
The monic sequence that shifts left under convolution with itself is the Catalan numbers with 130+ combinatorial interpretations. Here we establish a combinatorial interpretation f…
Some identities for the Catalan and Fine numbers
David Callan
We establish combinatorial interpretations of several identities for the Catalan and Fine numbers and, along the way, we present some new bijections of independent interest. Briefl…
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…