| Title:
|
On the height of order ideals (English) |
| Author:
|
Czédli, Gábor |
| Author:
|
Maróti, Miklós |
| Language:
|
English |
| Journal:
|
Mathematica Bohemica |
| ISSN:
|
0862-7959 (print) |
| ISSN:
|
2464-7136 (online) |
| Volume:
|
135 |
| Issue:
|
1 |
| Year:
|
2010 |
| Pages:
|
69-80 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
We maximize the total height of order ideals in direct products of finitely many finite chains. We also consider several order ideals simultaneously. As a corollary, a shifting property of some integer sequences, including digit sum sequences, is derived. (English) |
| Keyword:
|
order |
| Keyword:
|
product of chains |
| Keyword:
|
ideal of maximum height |
| Keyword:
|
digit sum sequence |
| MSC:
|
06A07 |
| MSC:
|
06D99 |
| idZBL:
|
Zbl 1224.06002 |
| idMR:
|
MR2643357 |
| DOI:
|
10.21136/MB.2010.140684 |
| . |
| Date available:
|
2010-07-20T18:23:46Z |
| Last updated:
|
2020-07-29 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/140684 |
| . |
| Reference:
|
[1] Bollobás, B., Leader, I.: Sums in the grid.Discrete Math. 162 (1996), 31-48. MR 1425777, 10.1016/S0012-365X(96)00303-2 |
| Reference:
|
[2] Czédli, G., Maróti, M., Schmidt, E. T.: On the scope of averaging for Frankl's conjecture.Order 26 (2009), 31-48. Zbl 1229.05259, MR 2487167, 10.1007/s11083-008-9105-5 |
| Reference:
|
[3] Davey, B. A., Priestley, H. A.: Introduction to Lattices and Order.Second edition, Cambridge University Press, New York (2002), xii+298. Zbl 1002.06001, MR 1902334 |
| Reference:
|
[4] Gel'fond, A. O.: Sur les nombres qui ont des propriétés additives et multiplicatives données.Acta Arith. 13 (1967/1968), 259-265. MR 0220693, 10.4064/aa-13-3-259-265 |
| Reference:
|
[5] Grätzer, G.: General Lattice Theory.New appendices with B. A. Davey, R. Freese, B. Ganter, M. Greferath, P. Jipsen, H. A. Priestley, H. Rose, E. T. Schmidt, S. E. Schmidt, F. Wehrung, R. Wille; Second edition. Birkhäuser, Basel (1998). MR 1670580 |
| Reference:
|
[6] Grätzer, G.: The congruences of a finite lattice.A proof-by-picture approach, Birkhäuser Boston, MA (2006), The Glossary of Notation is available as a pdf file at http://mirror.ctan.org/info/examples/Math$_-$into$_-$LaTeX-4/notation.pdf Zbl 1106.06001, MR 2177459 |
| Reference:
|
[7] Lindström, B.: On a combinatorial problem in number theory.Canad. Math. Bull. 8 (1965), 477-490. MR 0181604, 10.4153/CMB-1965-034-2 |
| . |
