Classification of Subsets of the Projective Line of Order Thirty Two and its Partitioned into Distinct Subsets
The aim of this paper is to find the inequivalent k-sets in the finite projective line of order thirty-two, PG(1,32). The number of projectively distinct 4-set is five and all of them are of type N(neither harmonic nor equianharmonic). The k-sets, k=4,…,11 have been done, where the number of projec...
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| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
| Published: |
University of Baghdad
2025-04-01
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| Series: | Ibn Al-Haitham Journal for Pure and Applied Sciences |
| Subjects: | |
| Online Access: | https://jih.uobaghdad.edu.iq/index.php/j/article/view/3705 |
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| Summary: | The aim of this paper is to find the inequivalent k-sets in the finite projective line of order thirty-two, PG(1,32). The number of projectively distinct 4-set is five and all of them are of type N(neither harmonic nor equianharmonic). The k-sets, k=4,…,11 have been done, where the number of projectively distinct are 5,11,53,148,481,1240,2964,6049, respectively. The k-sets k=12,..,17 classified depending on the projectively distinct 11-sets whose have non-trivial subgroups only, where the numbers of projectively distinct are 493,5077,2583,288,2412,697. The stabilizer group of each k-sets is computed. The kind of groups that computed for the k-sets are I, Z_2, Z_3, V_4, S_3, Z_2×Z_2×Z_2, Z_2×Z_2×Z_2×Z_2 and the large group is the dihedral group of order eleven appears when k is equal to eleven. Also, the projective line PG(1,32) is partitioned into three distinct 11-sets such that two of them are projectively equivalent, and into eight 4-sets of types N_1, N_2, N_3,. N_4, N_5, and into eight 4-sets four of them of type N_3, N_4.
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| ISSN: | 1609-4042 2521-3407 |