Recognition of prime posets and one of its applications
Khamis, Soheir;
Abstract
The paper contains a recognition algorithmic method for deciding whether a given
poset, P, is prime. The algorithm is designed to determine whether there exists a proper
P-autonomous set including specified two distinct elements of P. The steps are repeated
for all ordered pairs of distinct elements of P, if it is prime, in a polynomial time.
As an application of this test, the author counted the number of unlabeled prime
posets regarding heights up to 13 elements. The height counting algorithm depends on:
(1) Create the colexecographic list of all strictly upper triangular matrices satisfying the
bucket from; (2) Apply the given test to choose those corresponding to prime posets;
and (3) Enumerate the required number regarding height by summing the weights of
accepted matrices, that are also computed in the algorithm. The algorithm added to
height counting field, the original numbers of unlabeled 13-element prime posets of height
k; k · 13, and verified the previously known numbers of unlabeled n-element prime posets
of height k; 1 · k · n · 12, that have been introduced in [11].
poset, P, is prime. The algorithm is designed to determine whether there exists a proper
P-autonomous set including specified two distinct elements of P. The steps are repeated
for all ordered pairs of distinct elements of P, if it is prime, in a polynomial time.
As an application of this test, the author counted the number of unlabeled prime
posets regarding heights up to 13 elements. The height counting algorithm depends on:
(1) Create the colexecographic list of all strictly upper triangular matrices satisfying the
bucket from; (2) Apply the given test to choose those corresponding to prime posets;
and (3) Enumerate the required number regarding height by summing the weights of
accepted matrices, that are also computed in the algorithm. The algorithm added to
height counting field, the original numbers of unlabeled 13-element prime posets of height
k; k · 13, and verified the previously known numbers of unlabeled n-element prime posets
of height k; 1 · k · n · 12, that have been introduced in [11].
Other data
Title | Recognition of prime posets and one of its applications | Authors | Khamis, Soheir | Keywords | Counting, enumeration, partially ordered sets, finite poset, unlabeled, prime, height, and algorithm | Issue Date | 2006 | Journal | JOURNAL OF THE EGYPTIAN MATHEMATICAL SOCIETY |
Attached Files
File | Description | Size | Format | |
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Recognition of prime posets and one of its applications.pdf | 119.71 kB | Adobe PDF | View/Open |
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