A generalization of Pascal’s triangle using powers of base numbers

Gábor Kallós[1]

  • [1] Department of Computer Science Széchenyi István University Egyetem tér 1 Győr, H-9026 HUNGARY

Annales mathématiques Blaise Pascal (2006)

  • Volume: 13, Issue: 1, page 1-15
  • ISSN: 1259-1734

Abstract

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In this paper we generalize the Pascal triangle and examine the connections among the generalized triangles and powering integers respectively polynomials. We emphasize the relationship between the new triangles and the Pascal pyramids, moreover we present connections with the binomial and multinomial theorems.

How to cite

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Kallós, Gábor. "A generalization of Pascal’s triangle using powers of base numbers." Annales mathématiques Blaise Pascal 13.1 (2006): 1-15. <http://eudml.org/doc/10527>.

@article{Kallós2006,
abstract = {In this paper we generalize the Pascal triangle and examine the connections among the generalized triangles and powering integers respectively polynomials. We emphasize the relationship between the new triangles and the Pascal pyramids, moreover we present connections with the binomial and multinomial theorems.},
affiliation = {Department of Computer Science Széchenyi István University Egyetem tér 1 Győr, H-9026 HUNGARY},
author = {Kallós, Gábor},
journal = {Annales mathématiques Blaise Pascal},
language = {eng},
month = {1},
number = {1},
pages = {1-15},
publisher = {Annales mathématiques Blaise Pascal},
title = {A generalization of Pascal’s triangle using powers of base numbers},
url = {http://eudml.org/doc/10527},
volume = {13},
year = {2006},
}

TY - JOUR
AU - Kallós, Gábor
TI - A generalization of Pascal’s triangle using powers of base numbers
JO - Annales mathématiques Blaise Pascal
DA - 2006/1//
PB - Annales mathématiques Blaise Pascal
VL - 13
IS - 1
SP - 1
EP - 15
AB - In this paper we generalize the Pascal triangle and examine the connections among the generalized triangles and powering integers respectively polynomials. We emphasize the relationship between the new triangles and the Pascal pyramids, moreover we present connections with the binomial and multinomial theorems.
LA - eng
UR - http://eudml.org/doc/10527
ER -

References

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  1. Mary Basil, Pascal’s pyramid, Math. Teacher 61 (1968), 19-21 
  2. Richard C. Bollinger, A note on Pascal-T triangles, multinomial coefficients, and Pascal pyramids, The Fibonacci Quarterly 24.2 (1986), 140-144 Zbl0598.05011MR843962
  3. Boris A. Bondarenko, Generalized Pascal triangles and pyramids, their fractals, graphs and applications, (1993), The Fibonacci Association, Santa Clara Zbl0792.05001
  4. Sven J. Cyvin, Jon Brunvoll, Bjørg N. Cyvin, Isomer enumeration of unbranched catacondensed polygonal systems with pentagons and heptagons, Match 34 (1996), 109-121 Zbl0863.05006
  5. John E. Freund, Restricted occupancy theory – a generalization of Pascal’s triangle, Amer. Math. Monthly 63 (1956), 20-27 Zbl0070.01201MR74356
  6. Gábor Kallós, Generalizations of Pascal’s triangle, (1993) Zbl1172.11302
  7. Gábor Kallós, The generalization of Pascal’s triangle from algebraic point of view, Acta Acad. Paed. Agriensis XXIV (1997), 11-18 Zbl0886.05003
  8. Robert L. Morton, Pascal’s triangle and powers of 11, Math. Teacher 57 (1964), 392-394 
  9. Neil J. A. Sloane, On-line encyclopedia of integer sequences Zbl1044.11108

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