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On characteristic polynomials of the family of cobweb posets

E. Krot-Sieniawska
장전수학회 (Jangjeon Mathematical Society)|2008.12|Proceedings of the Jangjeon Mathematical Society(장전수학회 논문집) (Proceedings of the Jangjeon Mathematical Society)|제11권 제2호|pp. 105-111|DOI 10.17777/pjms.2008.11.2.001

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참고문헌

키워드

cobweb posetthe Mobius function of a posetWhitney numberscharacteristic polynomials.
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초록

This note is a response to one of problems posed by A.K. Kwa´sniewski in [7]. For {Pn}n≥0 being the sequence of finite cobweb sub-posets, the explicit formulas for corresponding sequence {Xn(t)}n≥0 of Pn’s characteristic polynomials are introduced. The recurrence relation defining arbitrary family {Xn(t)}n≥0 is derived.

Abstract

This note is a response to one of problems posed by A.K. Kwa´sniewski in [7]. For {Pn}n≥0 being the sequence of finite cobweb sub-posets, the explicit formulas for corresponding sequence {Xn(t)}n≥0 of Pn’s characteristic polynomials are introduced. The recurrence relation defining arbitrary family {Xn(t)}n≥0 is derived.

참고문헌 (13)

  1. Joni S. A., "From Sets to Functions: Three Elementary Examples", Discreta Mathematics, 37, pp.193~202 (1981)
  2. Krot E., "A note on Mobius function and Mobius inversion formula of Fibonacci Cobweb Poset", Bulletin de la Societe des Sciences et des Lettres de d (54), Serie: Recherches sur les Deformations, 44, pp.39~44
  3. Krot E., "The first ascent into the Fibonacci Cobweb Poset", Advanced Studies in Conterporary Mathematics, 11(2), pp.179~184 (2005)
  4. Krot-Sieniawska E., "On incidence algebras of cobweb posets, ArXiv:0802.3703", ~
  5. A. K. Kwasniewski, "Cobweb posets as noncommutative prefabs", Advanced Studies in Contemporary Mathematics, 14(1), pp.37~47 (2007), 장전수학회
  6. Kwa´sniewski A. K., "First observations on Prefab posets‘ Whitney numbers", Advances in Applied Clifford Algebras, 18(1), pp.57~73 (2008)
  7. Kwa´sniewski A. K., "On cobweb posets and their combinatorially admissible sequences", 2007 ISRAMA (2007)
  8. Kwa´sniewski A. K., "Cobweb posets - Recent Results", ISRAMA 2007 (2007)
  9. Rota G.-C., "On the Foundations of Combinatorial Theory: I. Theory of M¨obius Functions", Z. Wahrscheinlichkeitstheorie und Verw. Gebiete, 2, pp.340~368 (1964)
  10. Sagan B., "Why the characteristic polynomial factors", Bull. Amer. Math. Soc, 36, pp.113~134 (1999)
  12. Spiegel E., "Incidence algebras" (1997), Marcel Dekker, Inc
  13. Stanley R. P., "Enumerative Combinatorics, Volume I", pp.1986, Wadsworth& Brooks

관련 논문AI추천

On incidence algebras description of cobweb posetsEwa Krot-Sieniawska장전수학회 · Proceedings of the Jangjeon Mathematical Society(장전수학회 논문집)2013 · 제16권 제1호On cobweb posets tilling problemMaciej Dziemianczuk장전수학회 · Advanced Studies in Contemporary Mathematics2008 · 제16권 제2호On cobweb posets and their combinatorially admissible sequencesA. K. Kwaśniewski장전수학회 · Advanced Studies in Contemporary Mathematics2009 · 제18권 제1호Cobweb posets-Recent ResultsA Krzysztof Kwasniewski, M. Dziemianczuk장전수학회 · Advanced Studies in Contemporary Mathematics2008 · 제16권 제2호Some polynomials with unimodular rootsArturas Dubickas대한수학회 · 대한수학회보2022 · 제59권 제5호ENUMERATION OF OPTIMALLY LABELLED n-POSETS OF LINEAR DISCREPANCY TWO채갑병장전수학회 · Proceedings of the Jangjeon Mathematical Society(장전수학회 논문집)2017 · 제20권 제4호

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