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2019 | 18 | 93-122

Tytuł artykułu

Binomial sequences

Autorzy

Treść / Zawartość

Warianty tytułu

Języki publikacji

EN

Abstrakty

EN
We present a description of all binomial sequences of polynomials in one variable over a field of characteristic zero.

Rocznik

Tom

18

Strony

93-122

Opis fizyczny

Daty

wydano
2019-07-11

Twórcy

  • Nicolaus Copernicus University, Faculty of Mathematics and Computer Science

Bibliografia

  • Aceto, Lidia and Isabel Cação. "A matrix approach to Sheffer polynomials." J. Math. Anal. Appl. 446, no. 1 (2017): 87-100.
  • Berthelot, Pierre Cohomologie cristalline des schémas de caractéristique p > 0. Vol. 407 of Lecture Notes in Mathematics. Berlin-New York: Springer-Verlag, 1974.
  • Brand, Louis. "Binomial expansions in factorial powers." Amer. Math. Monthly 67 (1960): 953-957.
  • Brown, J.W. "On zero type sets of Laguerre polynomials." Duke Math. J. 35 (1968): 821-823.
  • Di Bucchianico, A. Probabilistic and analytical aspects of the umbral calculus. Vol. 119 CWI Tract. Amsterdam: Stichting Mathematisch Centrum, Centrum voor Wiskunde en Informatica, 1997
  • Carlitz, L. "Some generating functions for Laguerre polynomials." Duke Math. J. 35 (1968), 825-827.
  • Comtet, Louis. Advanced combinatorics. The art of finite and infinite expansions. Dordrecht: D. Reidel Publishing Co., 1974.
  • Ekhad, Shalosh B. and John E. Majewicz. "A short WZ-style proof of Abel’s identity." Electron. J. Combin. 3, no. 2 (1996): Research Paper 16, approx. 1 p.
  • Foata, Dominique. "Enumerating k-trees." Discrete Math. 1, no. 2 (1971/72): 181-186.
  • Graham, Ronald L., Donald E. Knuth and Oren Patashnik. Concrete mathematics. A foundation for computer science. Reading, MA: Addison-Wesley Publishing Company, 1989.
  • Huang, Fengying and Bolian Liu. "The Abel-type polynomial identities." Electron. J. Combin. 17, no. 1, (2010): Research Paper 10, 7 pp.
  • Kisil, Vladimir V. "Polynomial sequences of binomial type and path integrals." Ann. Comb. 6, no. 1, (2002): 45-56.
  • Krall, H.L. "Polynomials with the binomial property." Amer. Math. Monthly 64 (1957): 342-343.
  • Lipnowski, M. "A solution of Problem 310." Vol. 5 of Olymon – Mathematical Olympiads’ Correspondence Program. Canada: Canadian Mathematical Society, 2004.
  • Mihoubi, Miloud. "Bell polynomials and binomial type sequences." Discrete Math. 308, no. 12 (2008): 2450-2459.
  • Młotkowski, Wojciech and Romanowicz, Anna. "A family of sequences of binomial type." Probab. Math. Statist. 33, no. 2 (2013): 401-408.
  • Nowicki, Andrzej. Arithmetic functions Vol.5 of Podróze po Imperium Liczb. Torun, Olsztyn: Wydawnictwo OWSIiZ, 2012.
  • Nowicki, Andrzej. Factorials and binomial coefficiens, Vol. 11 of Podróze po Imperium Liczb. Torun, Olsztyn: Wydawnictwo OWSIiZ, 2013.
  • Petrullo, Pasquale. "Outcomes of the Abel identity." Mediterr. J. Math. 10, no. 3 (2013): 1141-1150.
  • Roman, Steven M. and Gian-Carlo Rota. "The umbral calculus." Advances in Math. 27, no. 2 (1978): 95-188.
  • Rota, Gian-Carlo, D. Kahaner and A. Odlyzko, "On the foundations of combinatorial theory. VIII. Finite operator calculus." J. Math. Anal. Appl. 42 (1973): 84-760.
  • Rota, Gian-Carlo, Jianhong Shen and Brian D. Taylor. "All polynomials of binomial type are represented by Abel polynomials." Ann. Scuola Norm. Sup. Pisa Cl. Sci. (4) 25, no. 3-4 (1997): 731-738.
  • Schneider, Jonathan. "Polynomial sequences of binomial-type arising in graph theory." Electron. J. Combin. 21, no. 1 (2014): Paper 1.43, 17 pp.
  • Sheffer, I.M. "Some properties of polynomial sets of type zero." Duke Math. J. 5 (1939): 590-622.
  • Shukla, A.K. and S.J. Rapeli. "An extension of Sheffer polynomials." Proyecciones 30, no. 2 (2011): 265-275.
  • Sykora, S. "An Abel’s identity and its corollaries." Preprint, 2014.
  • Zheng, G. "A solution of Problem 310." Vol. 5 of Olymon – Mathematical Olympiads’ Correspondence Program. Canada: Canadian Mathematical Society, 2004.

Typ dokumentu

Bibliografia

Identyfikatory

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bwmeta1.element.ojs-issn-2300-133X-year-2019-volume-18-article-7947
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