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Tytuł artykułu

Variation Statistics on Compositions

Wybrane pełne teksty z tego czasopisma
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Języki publikacji
EN
Abstrakty
EN
In this paper we consider the absolute variation statistics of a compositionσ=σ_1...σ_m of n which is a measure of the sum of absolute differences between each consecutive pair of parts in a composition. This and some related statistics which we discuss, can also be interpreted within the context of bargraph polygons and bargraph walks of area n. In this context, absolute variation corresponds to the interior vertical perimeter of a bargraph polygon or to the interior vertical length of a bargraph walk.
Wydawca
Rocznik
Strony
1--17
Opis fizyczny
Bibliogr. 17 poz.
Twórcy
autor
autor
  • The John Knopfmacher Centre for Applicable Analysis and Number Theory, Department of Mathematics, University of the Witwatersrand, P. O. Wits, 2050, Johannesburg, South Africa, arnold.knopfmacher@wits.ac.za
Bibliografia
  • [1] Andrews, G. E., Askey, R., Roy, R.: Special functions, Encyclopedia of Mathematics and its Applications 71, Cambridge University Press, Cambridge, 1999.
  • [2] Bousquet-Melou,M., Rechnitzer, A.: The site-perimeter of bargraphs. Adv. in Appl.Math. 31, 2003, 86-112.
  • [3] Chao, G. C., Liang,W. Q.: Arranging n distinct numbers on a line or a circle to reach extreme total variations, Europ. J. Combin. 13, 1992, 325-334.
  • [4] Cohen, G. L., Tonkes, E.: Dartboard arrangements, Elect. J. Combin. 8(2), 2001, #R4.
  • [5] Curtis, S. A.: Darts and hoopla board design, Inform. Proc. Lett. 92, 2004, 53-56.
  • [6] Hitczenko, P., Knopfmacher,A.: Gap-free compositions and gap-free samples of geometric randomvariables, Discrete Math. 294, 2005, 225-239.
  • [7] Hitczenko, P., Louchard, G.: Distinctness of compositions of an integer: a probabilistic analysis, Random Struct. Alg. 19, 2001, 407-437.
  • [8] Heubach, S., Mansour, T.: Counting rises, levels, and drops in compositions, Integers Elec. J. Comb. Num. Th. 5, 2005, Article A11.
  • [9] Heubach, S., Mansour, T.: Avoiding patterns of length three in compositions and multiset permutations, Adv. Appl. Math. 36, 2006, 156-174.
  • [10] Hwang, H. K., Yeh, Y. N.: Measures of distinctness for random partitions and compositions of an integer, Adv. App. Math. 3, 1997, 378-414.
  • [11] Knopfmacher, A., Mays, M. E.: Compositions with m distinct parts, Ars Combinatoria 53, 1999, 111-128.
  • [12] Liao, Y. J., Shieh, M. Z., Tsai, S. C.: Arranging numbers on circles to reach maximum total variations, Elect. J. Combin. 14, 2007, #R47.
  • [13] Mansour, T., Enumeration of words by the sum of differences between adjacent letters, Discrete Math. Theor. Comp. Sci. 11:1, 2009, 173-186.
  • [14] Rawlings, D., Tiefenbruck,M.: Consecutive patterns: frompermutations to column-convex polyominoes and back, Elect. J. Combin. 17(1), 2010, #R62.
  • [15] Sloane, N. J. A.: The On-Line Encyclopedia of Integer Sequences, 2007, published electronically at www.research.att.com/ njas/sequences/.
  • [16] Savage, C., Wilf, H.: Pattern avoidance in compositions and multiset permutations, Adv. Appl. Math. 36, 2006, 194-201.
  • [17] Janse van Rensburg, E. J., Rechnitzer, A.: Exchange Symmetries in Motzkin Path and Bargraph models of Copolymer Adsorption, Elect. J. Combin. 9, 2002, #R20.
Typ dokumentu
Bibliografia
Identyfikator YADDA
bwmeta1.element.baztech-article-BUS8-0026-0001
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