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- articleMay 2006
Further combinatorial identities deriving from the nth power of a 2 × 2 matrix
Discrete Applied Mathematics (DAMA), Volume 154, Issue 8Pages 1301–1308In this paper we use a formula for the nth power of a 2 × 2 matrix A (in terms of the entries in A) to derive various combinatorial identities. Three examples of our results follow. (1) We show that if m and n are positive integers and s ∈ {0,1,2,..., ⌊(...
- articleNovember 2002
q-Pell sequences and two identities of V.A. Lebesgue
Discrete Mathematics (DMAT), Volume 257, Issue 1Pages 125–142https://doi.org/10.1016/S0012-365X(01)00475-7We examine a pair of Rogers-Ramanujan type identities of Lebesgue, and give polynomial identities for which the original identities are limiting cases. The polynomial identities turn out to be q-analogs of the Pell sequence. Finally, we provide ...
- articleJuly 2000
Invariant Cubature Formulae for Spheres and Balls by Combinatorial Methods
SIAM Journal on Numerical Analysis (SINUM), Volume 38, Issue 2Pages 626–638https://doi.org/10.1137/S003614299935543XInvariant cubature formulae for a class of weight functions on the simplex $T^d$ are derived using combinatorial methods, extending the formulae in [Grundmann and Möller, SIAM J. Numer Anal., 15 (1978), pp. 282--290] for the unit weight function on Td. ...
- articleDecember 1997
Order statistics applications to queueing and scheduling problems
Queueing Systems: Theory and Applications (QSYS), Volume 27, Issue 3/4Pages 325–350https://doi.org/10.1023/A:1019126501541We prove several basic combinatorial identities and use them in two applications: the queue inference engine (QIE) and earliest due date rule (EDD) scheduling. Larson (1990) introduced the QIE. His objective was to deduce the behavior of a multiserver ...
- articleFebruary 1997