On extensions, linear extensions, upsets and downsets of ordered sets

Corrêa, Ricardo C.; Szwarcfiter, Jayme Luiz

doi:10.1016/j.disc.2004.12.007

Cited by 2 publications

(2 citation statements)

References 11 publications

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“…Counting linear extensions of a general poset S was demonstrated to be #P-complete [13]. Several algorithms and strategies for generating linear extensions of non-structured posets were reported over the years [7,12,14,27,39,48,49,51,61,63,70,72].…”

Section: Generation Of the Jordan-hölder Set L(s) Of Smentioning

confidence: 99%

ZZ Polynomials of Regular m-tier Benzenoid Strips as Extended Strict Order Polynomials of Associated Posets Part 2. Guide to Practical Computation

Langner¹,

Witek²

2022

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We present an algorithm for computing the ZZ polynomial of an arbitrary m-tier regular strip of length n. Our approach is based on the equivalence between the ZZ polynomial ZZ(S, x) of a regular benzenoid strip S and the extended strict order polynomial E • S (n, 1 + x) of the corresponding poset S, demonstrated formally in Part 1 of the current series of papers. The process of computing ZZ(S, x) in the form of E • S (n, 1 + x) reduces to four, fully automatable steps: (i) Construction of the poset S corresponding to S. (ii) Construction of the Jordan-Hölder set L(S) of linear extensions of S. (iii) Computing the number des(w) of descents in each w ∈ L(S). (iv) Computing the number fix S (w) of fixed labels in each w ∈ L(S). The ZZ polynomial of S can then be expressed in the following formwhere |S| denotes the number of elements in S. Practical applications of the algorithm are illustrated with a few examples. The complete account of ZZ polynomials of regular m-tier benzenoid strips S with m = 1-6 computed using the introduced algorithm is presented in Part 3 of the current series of papers.

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Section: Generation Of the Jordan-hölder Set L(s) Of Smentioning

confidence: 99%

ZZ Polynomials of Regular m-tier Benzenoid Strips as Extended Strict Order Polynomials of Associated Posets Part 2. Guide to Practical Computation

Langner¹,

Witek²

2022

Match

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“…Enumerating the extensions of a partially ordered set is a typical search problem, in which the arrangements are all the binary relations that can be defined on a set given as input and the solutions are only the relations that are partial orders containing the given partial order on the input set [8]. Search problems are amenable to a distributed treatment when the set of possible arrangements can be appropriately partitioned among the nodes of the distributed system.…”

Section: Search Problemsmentioning

confidence: 99%

Partially ordered distributed computations on asynchronous point-to-point networks

Corrêa

Barbosa

2009

Parallel Computing

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Asynchronous executions of a distributed algorithm differ from each other due to the nondeterminism in the order in which the messages exchanged are handled. In many situations of interest, the asynchronous executions induced by restricting nondeterminism are more efficient, in an application-specific sense, than the others. In this work, we define partially ordered executions of a distributed algorithm as the executions satisfying some restricted orders of their actions in two different frameworks, those of the so-called event-and pulse-driven computations. The aim of these restrictions is to characterize asynchronous executions that are likely to be more efficient for some important classes of applications.Also, an asynchronous algorithm that ensures the occurrence of partially ordered executions is given for each case. Two of the applications that we believe may benefit from the restricted nondeterminism are backtrack search, in the event-driven case, and iterative algorithms for systems of linear equations, in the pulse-driven case.

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On extensions, linear extensions, upsets and downsets of ordered sets

Cited by 2 publications

References 11 publications

ZZ Polynomials of Regular m-tier Benzenoid Strips as Extended Strict Order Polynomials of Associated Posets Part 2. Guide to Practical Computation

ZZ Polynomials of Regular m-tier Benzenoid Strips as Extended Strict Order Polynomials of Associated Posets Part 2. Guide to Practical Computation

Partially ordered distributed computations on asynchronous point-to-point networks

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