On the height of order ideals

Gábor Czédli; Miklós Maróti

Mathematica Bohemica (2010)

  • Volume: 135, Issue: 1, page 69-80
  • ISSN: 0862-7959

Abstract

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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.

How to cite

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Czédli, Gábor, and Maróti, Miklós. "On the height of order ideals." Mathematica Bohemica 135.1 (2010): 69-80. <http://eudml.org/doc/38112>.

@article{Czédli2010,
abstract = {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.},
author = {Czédli, Gábor, Maróti, Miklós},
journal = {Mathematica Bohemica},
keywords = {order; product of chains; ideal of maximum height; digit sum sequence; order ideals; product of chains; ideal of maximum height; digit sum sequence},
language = {eng},
number = {1},
pages = {69-80},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {On the height of order ideals},
url = {http://eudml.org/doc/38112},
volume = {135},
year = {2010},
}

TY - JOUR
AU - Czédli, Gábor
AU - Maróti, Miklós
TI - On the height of order ideals
JO - Mathematica Bohemica
PY - 2010
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 135
IS - 1
SP - 69
EP - 80
AB - 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.
LA - eng
KW - order; product of chains; ideal of maximum height; digit sum sequence; order ideals; product of chains; ideal of maximum height; digit sum sequence
UR - http://eudml.org/doc/38112
ER -

References

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  1. Bollobás, B., Leader, I., 10.1016/S0012-365X(96)00303-2, Discrete Math. 162 (1996), 31-48. (1996) MR1425777DOI10.1016/S0012-365X(96)00303-2
  2. Czédli, G., Maróti, M., Schmidt, E. T., 10.1007/s11083-008-9105-5, Order 26 (2009), 31-48. (2009) Zbl1229.05259MR2487167DOI10.1007/s11083-008-9105-5
  3. Davey, B. A., Priestley, H. A., Introduction to Lattices and Order, Second edition, Cambridge University Press, New York (2002), xii+298. (2002) Zbl1002.06001MR1902334
  4. Gel'fond, A. O., 10.4064/aa-13-3-259-265, Acta Arith. 13 (1967/1968), 259-265. MR0220693DOI10.4064/aa-13-3-259-265
  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). (1998) MR1670580
  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/MathintoLaTeX-4/notation.pdf (2006) Zbl1106.06001MR2177459
  7. Lindström, B., 10.4153/CMB-1965-034-2, Canad. Math. Bull. 8 (1965), 477-490. (1965) MR0181604DOI10.4153/CMB-1965-034-2

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