Shade in Compositions of Integers

被引:0
作者
Blecher, Aubrey [1 ]
Knopfmacher, Arnold [1 ]
Mays, Michael [2 ]
机构
[1] Univ Witwatersrand, John Knopfmacher Ctr Applicable Anal & Number Theo, Sch Math, Private Bag 3,PO Wits, ZA-2050 Johannesburg, South Africa
[2] West Virginia Univ, Sch Math & Data Sci, Morgantown, WV 26506 USA
关键词
generating function; shade; composition; PATHS;
D O I
暂无
中图分类号
O1 [数学];
学科分类号
0701 ; 070101 ;
摘要
Integer compositions of n can be viewed as bargraphs, in which the ith part of the composition xi is given by the ith column of the bargraph with xi cells. The sun is at infinity in the northwest of our two-dimensional model, and each composition casts a shadow in accordance with the rules of physics. We find the number of unit squares in this shadow (but not being part of the composition) through a bivariate generating function tracking composition size and shadow.
引用
收藏
页数:11
相关论文
共 9 条
[1]   SHEDDING LIGHT ON WORDS [J].
Archibald, Margaret ;
Blecher, Aubrey ;
Brennan, Charlotte ;
Knopfmacher, Arnold ;
Mansour, Toufik .
APPLICABLE ANALYSIS AND DISCRETE MATHEMATICS, 2017, 11 (01) :216-231
[2]  
BLECHER A., 2018, Online Journal of Analytic Combinatorics, V13
[3]  
Blecher A., Casting light on partitions
[4]  
Blecher A, 2012, ARS COMBINATORIA, V106, P213
[5]   Skew Dyck paths, area, and superdiagonal bargraphs [J].
Deutsch, Emeric ;
Munarini, Emanuele ;
Rinaldi, Simone .
JOURNAL OF STATISTICAL PLANNING AND INFERENCE, 2010, 140 (06) :1550-1562
[6]   On Carlitz compositions [J].
Knopfmacher, A ;
Prodinger, H .
EUROPEAN JOURNAL OF COMBINATORICS, 1998, 19 (05) :579-589
[7]  
Prodinger H, 2018, AUSTRALAS J COMB, V72, P509
[8]  
Sloane Neil J. A., 2023, The on-line encyclopedia of integer sequences
[9]   Adsorbing bargraph paths in a q-wedge [J].
van Rensburg, EJJ .
JOURNAL OF PHYSICS A-MATHEMATICAL AND GENERAL, 2005, 38 (40) :8505-8525