| Title:
|
On forbidden configuration of pseudomodular lattices (English) |
| Author:
|
Dhake, Manoj |
| Author:
|
Ballal, Sachin |
| Author:
|
Kharat, Vilas |
| Author:
|
Shewale, Rupesh S. |
| Language:
|
English |
| Journal:
|
Mathematica Bohemica |
| ISSN:
|
0862-7959 (print) |
| ISSN:
|
2464-7136 (online) |
| Volume:
|
150 |
| Issue:
|
1 |
| Year:
|
2025 |
| Pages:
|
99-108 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
We characterize the pseudomodular lattices by means of a forbidden configuration. (English) |
| Keyword:
|
forbidden configuration |
| Keyword:
|
pseudomodular lattice |
| Keyword:
|
semimodular lattice |
| MSC:
|
06C10 |
| MSC:
|
06C99 |
| DOI:
|
10.21136/MB.2024.0126-23 |
| . |
| Date available:
|
2025-02-20T16:11:00Z |
| Last updated:
|
2025-02-20 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/152878 |
| . |
| Reference:
|
[1] Birkhoff, G.: Lattice Theory.Colloquium Publications 25. AMS, Providence (1967). Zbl 0153.02501, MR 0227053, 10.1090/coll/025 |
| Reference:
|
[2] Björner, A., Lovász, L.: Pseudomodular lattices and continuous matroids.Acta Sci. Math. 51 (1987), 295-308. Zbl 0643.05023, MR 0940934 |
| Reference:
|
[3] Dress, A., Hochstättler, W., Kern, W.: Modular substructures in pseudomodular lattices.Math. Scand. 74 (1994), 9-16. Zbl 0810.06007, MR 1277784, 10.7146/math.scand.a-12475 |
| Reference:
|
[4] Dress, A., Lovász, L.: On some combinatorial properties of algebraic matroids.Combinatorica 7 (1987), 39-48. Zbl 0627.05016, MR 0905150, 10.1007/BF02579199 |
| Reference:
|
[5] Grätzer, G.: General Lattice Theory.Pure and Applied Mathematics 75. Academic Press, New York (1978). Zbl 0436.06001, MR 0509213, 10.1007/978-3-0348-7633-9 |
| Reference:
|
[6] Haskins, L., Gudder, S.: Heights on posets and graphs.Discrete Math. 2 (1972), 357-382. Zbl 0238.06002, MR 0306059, 10.1016/0012-365X(72)90014-3 |
| Reference:
|
[7] Stern, M.: Semimodular Lattices: Theory and Applications.Encyclopedia of Mathematics and Its Applications 73. Cambridge University Press, Cambridge (1999). Zbl 0957.06008, MR 1695504, 10.1017/CBO9780511665578 |
| Reference:
|
[8] Teo, K. L.: Diagrammatic characterizations of semimodular lattices of finite length.Southeast Asian Bull. Math. 12 (1988), 135-140. Zbl 0664.06006, MR 0981353 |
| . |
