2 citations · 3 across the 2 of their papers we have counts for
6 papers
Crossings and Nestings of Matchings and Partitions
William Y. C. Chen, Eva Y. P. Deng, Rosena R. X. Du +2
We present results on the enumeration of crossings and nestings for matchings and set partitions. Using a bijection between partitions and vacillating tableaux, we show that if we…
Generating functions for moments of the quasi-nilpotent DT-operator
Ken Dykema, Catherine Yan
We prove a recursion formula for generating functions of certain renormalizations of *-moments of the DT(δ_0,1)-operator T, involving an operation \odot on formal power series and…
Apollonian Circle Packings: Geometry and Group Theory III. Higher Dimensions
R. L. Graham, J. C. Lagarias, C. L. Mallows +2
This paper gives -dimensional analogues of the Apollonian circle packings in parts I and II. We work in the space $\sM_{\dd}^n$ of all -dimensional oriented Descartes configu…
Apollonian Circle Packings: Geometry and Group Theory II. Super-Apollonian Group and Integral Packings
R. L. Graham, J. C. Lagarias, C. L. Mallows +2
Apollonian circle packings arise by repeatedly filling the interstices between four mutually tangent circles with further tangent circles. Such packings can be described in terms o…
Apollonian Circle Packings: Geometry and Group Theory I. The Apollonian Group
R. L. Graham, J. C. Lagarias, C. L. Mallows +2
Apollonian circle packings arise by repeatedly filling the interstices between four mutually tangent circles with further tangent circles. We observe that there exist Apollonian pa…
Quasifinite representations of classical Lie subalgebras of W_{1+infty}
Victor G. Kac, Weiqiang Wang, Catherine H. Yan
We show that there are precisely two, up to conjugation, anti-involutions sigma_{\pm} of the algebra of differential operators on the circle preserving the principal gradation. We…