Coxeter spectral classification of almost TP -critical one-peak posets using symbolic and numeric computations

Polak, Agnieszka; Simson, Daniel

doi:10.1016/j.laa.2013.12.018

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Cited by 15 publications

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“…Their number is 132 up to isomorphism and 75 up to isomorphism and duality. Later A. Polak and D. Simson [10] offered an alternative way of describing the P -critical posets by using computer algebra tools; in doing this, they also described the Tits P -critical posets.…”

Section: Resultsmentioning

confidence: 99%

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On classifying the non-Tits P-critical posets

Бондаренко

Styopochkina²

2021

ADM

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In 2005, the authors described all introduced by them P-critical posets (minimal finite posets with the quadratic Tits form not being positive); up to isomorphism, their number is 132 (75 if duality is considered). Later (in 2014) A. Polak and D. Simson offered an alternative way of proving by using computer algebra tools. In doing this, they defined and described the Tits P-critical posets as a special case of the P-critical posets. In this paper we classify all the non-Tits P-critical posets without complex calculations and without using the list of all P-critical ones.

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Section: Resultsmentioning

confidence: 99%

“…Later A. Polak and D. Simson [10] offered an alternative way of describing the P -critical posets by using computer algebra tools (mainly symbolic computation in Maple and numeric computation in C#). In doing this, they deőned and described the Tits P -critical posets as a special case of the P -critical ones.…”

Section: Introductionmentioning

confidence: 99%