Visible point vector summations from hypercube and hyperpyramid lattices
New identities are given, based on ideas related to visible (from the origin) point vectors. Each result was found from summing on vpv lattices dividing space into radial regions from the origin. This is related to recent work by the author in which new partition type infinite products were deriv...
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| Format: | Article |
| Language: | English |
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Wiley
1998-01-01
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| Series: | International Journal of Mathematics and Mathematical Sciences |
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| Online Access: | http://dx.doi.org/10.1155/S0161171298001033 |
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| _version_ | 1832568250384252928 |
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| author | Geoffrey B. Campbell |
| author_facet | Geoffrey B. Campbell |
| author_sort | Geoffrey B. Campbell |
| collection | DOAJ |
| description | New identities are given, based on ideas related to visible (from the origin) point vectors. Each result was found from summing on vpv lattices dividing space
into radial regions from the origin. This is
related to recent work by the author in which new partition type infinite products were derived. Also
recently, Baake et al [3] and Mosseri [14] considered the 2-D
visible lattice points as part of an optical
experiment in which the so-called Optical Fourier Transform was applied. Many of the techniques
espoused in Glasser and Zucker [11], and in Ninham et al [15] involving Mellin and Möbius inversions
are applicable also to the current paper. |
| format | Article |
| id | doaj-art-d9740349058a4d3d83ea7b7aa8cf1d37 |
| institution | Kabale University |
| issn | 0161-1712 1687-0425 |
| language | English |
| publishDate | 1998-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | International Journal of Mathematics and Mathematical Sciences |
| spelling | doaj-art-d9740349058a4d3d83ea7b7aa8cf1d372025-02-03T00:59:29ZengWileyInternational Journal of Mathematics and Mathematical Sciences0161-17121687-04251998-01-0121474174810.1155/S0161171298001033Visible point vector summations from hypercube and hyperpyramid latticesGeoffrey B. Campbell0Centre for Mathematics and its Applications, School of Mathematical Sciences, Australian National University, Canberra ACT 0200, AustraliaNew identities are given, based on ideas related to visible (from the origin) point vectors. Each result was found from summing on vpv lattices dividing space into radial regions from the origin. This is related to recent work by the author in which new partition type infinite products were derived. Also recently, Baake et al [3] and Mosseri [14] considered the 2-D visible lattice points as part of an optical experiment in which the so-called Optical Fourier Transform was applied. Many of the techniques espoused in Glasser and Zucker [11], and in Ninham et al [15] involving Mellin and Möbius inversions are applicable also to the current paper.http://dx.doi.org/10.1155/S0161171298001033Combinatorial identitiesCombinatorial number theoryLattice points in specified regionsPartitions (elementary number theory). |
| spellingShingle | Geoffrey B. Campbell Visible point vector summations from hypercube and hyperpyramid lattices International Journal of Mathematics and Mathematical Sciences Combinatorial identities Combinatorial number theory Lattice points in specified regions Partitions (elementary number theory). |
| title | Visible point vector summations from hypercube and hyperpyramid lattices |
| title_full | Visible point vector summations from hypercube and hyperpyramid lattices |
| title_fullStr | Visible point vector summations from hypercube and hyperpyramid lattices |
| title_full_unstemmed | Visible point vector summations from hypercube and hyperpyramid lattices |
| title_short | Visible point vector summations from hypercube and hyperpyramid lattices |
| title_sort | visible point vector summations from hypercube and hyperpyramid lattices |
| topic | Combinatorial identities Combinatorial number theory Lattice points in specified regions Partitions (elementary number theory). |
| url | http://dx.doi.org/10.1155/S0161171298001033 |
| work_keys_str_mv | AT geoffreybcampbell visiblepointvectorsummationsfromhypercubeandhyperpyramidlattices |