| Title:
|
Delannoy and tetrahedral numbers (English) |
| Author:
|
Schröder, Joachim |
| Language:
|
English |
| Journal:
|
Commentationes Mathematicae Universitatis Carolinae |
| ISSN:
|
0010-2628 (print) |
| ISSN:
|
1213-7243 (online) |
| Volume:
|
48 |
| Issue:
|
3 |
| Year:
|
2007 |
| Pages:
|
389-394 |
| . |
| Category:
|
math |
| . |
| Summary:
|
We establish an identity between Delannoy numbers and tetrahedral numbers of arbitrary dimension. (English) |
| Keyword:
|
Delannoy numbers |
| Keyword:
|
tetrahedral numbers |
| Keyword:
|
king's walk |
| Keyword:
|
coordination number |
| Keyword:
|
crystal ball |
| MSC:
|
05A10 |
| MSC:
|
05A15 |
| MSC:
|
05A19 |
| idZBL:
|
Zbl 1199.05003 |
| idMR:
|
MR2374122 |
| . |
| Date available:
|
2009-05-05T17:03:41Z |
| Last updated:
|
2012-05-01 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/119667 |
| . |
| Reference:
|
[1] Aigner M.: Diskrete Mathematik.Vieweg, Braunschweig, 1993. Zbl 1109.05001, MR 1243412 |
| Reference:
|
[2] Banderier C., Schwer S.R.: Why Delannoy numbers?.J. Statist. Plann. Inference 135 1 (2005), 40-54; CoRR math.CO/0411128: (2004). Zbl 1074.01012, MR 2202337 |
| Reference:
|
[3] Conway J.H., Sloane N.J.A.: Low dimensional lattices VII: Coordination sequences.Proc. Royal Soc. London Ser. A 453 (1997), 1966 2369-2389; citeseer.ist.psu.edu/article/conway96lowdimensional.html. Zbl 1066.11505, MR 1480120 |
| Reference:
|
[4] Delannoy H.: Emploi de l'échiquier pour la résolution de certains problèmes de probabilités.Association Francaise pour l'Avancement des Sciences, Bordeaux XXIV (1895), 70-90. |
| Reference:
|
[5]
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| Reference:
|
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| Reference:
|
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| Reference:
|
[8] Schröder J.: Generalized Schröder numbers and the rotation principle.preprint, 2007. MR 2346050 |
| Reference:
|
[9] Stanley R.P.: Enumerative Combinatorics.Vol. 2, Cambridge University Press, Cambridge, 1999. Zbl 0978.05002, MR 1676282 |
| Reference:
|
[10] Vassilev M., Atanassov K.: On Delan$[$n$]$oy numbers.Annuaire Univ. Sofia Fac. Math. Inform. 81 (1987), 153-162. MR 1291893 |
| . |
