Abstract
Take an entry X inside m-dimensional Pascal’s pyramid consisting of m-nomial coefficients. We call a set of successive r entries starting A on the half line XA a ray of length r with center X, where A is one of the m(m + 1) entries surrounding X, and the union of nonempty set of rays with center X a star with center X. When, in the following, we assume that a star S is translatable in parallel with its center in Pascal’s pyramid, we sometimes use the same word “star” instead of “star configuration” for brevity. For a configuration of two sets of entries U and V in the pyramid, we say that U covers V w.r.t. LCM if the equality LCM U ⋃ V = LCM U always holds independent of the location of U and V as long as they are contained in the pyramid and their relative location is unchanged. We say that a star S is a center covering star w.r.t. LCM if it covers its center in the above sense, and it is minimal if it does not contain any such center covering star with the same center which is a proper subset of S.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Ando, S. “A Triangular Array with Hexagon Property, Dual to Pascal’s Triangle”. Applications of Fibonacci Numbers, Volume 2. Edited by G.E. Bergum, A.N. Philippou and A.F. Horadam. Kluwer Academic Publishers, Dordrecht, The Netherlands, 1988, pp. 61–67.
Ando, S. and Sato, D. “On the Proof of GCD and LCM Equalities Concerning the Generalized Binomial and Multinomial Coefficients”. Applications of Fibonacci Numbers. Volume 4. Edited by G.E. Bergum, A.N. Philippou and A.F. Horadam. Kluwer Academic Publishers, Dordrecht, The Netherlands, 1991, pp. 9–16.
Ando, S. and Sato, D. “On the Minimal Center Covering Stars with Respect to GCD in Pascal’s Pyramid and Its Generalizations”. Applications of Fibonacci Numbers. Volume 5. Edited by G.E. Bergum, A.N. Philippou and A.F. Horadam. Kluwer Academic Publishers, Dordrecht, The Netherlands, 1993, pp. 37–43.
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 1996 Kluwer Academic Publishers
About this chapter
Cite this chapter
Ando, S., Sato, D. (1996). Minimal Center Covering Stars with Respect to LCM in Pascal’s Pyramid and its Generalizations. In: Bergum, G.E., Philippou, A.N., Horadam, A.F. (eds) Applications of Fibonacci Numbers. Springer, Dordrecht. https://doi.org/10.1007/978-94-009-0223-7_2
Download citation
DOI: https://doi.org/10.1007/978-94-009-0223-7_2
Publisher Name: Springer, Dordrecht
Print ISBN: 978-94-010-6583-2
Online ISBN: 978-94-009-0223-7
eBook Packages: Springer Book Archive