Enumeration of pyramids of one-dimensional pieces of arbitrary fixed integer length
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Enumeration of pyramids of one-dimensional pieces of arbitrary fixed integer length. / Durhuus, Bergfinnur; Eilers, Søren.
Museum Tusculanum, 2009.Research output: Working paper › Research
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TY - UNPB
T1 - Enumeration of pyramids of one-dimensional pieces of arbitrary fixed integer length
AU - Durhuus, Bergfinnur
AU - Eilers, Søren
N1 - Keywords: math.CO; 05A15; 82B41
PY - 2009
Y1 - 2009
N2 - We consider pyramids made of one-dimensional pieces of fixed integer length a and which may have pairwise overlaps of integer length from 1 to a. We prove that the number of pyramids of size m, i.e. consisting of m pieces, equals (am-1,m-1) for each a >= 2. This generalises a well known result for a = 2. A bijective correspondence between so-called right (or left) pyramids and a-ary trees is pointed out, and it is shown that asymptotically the average width of pyramids is proportional to the square root of the size.
AB - We consider pyramids made of one-dimensional pieces of fixed integer length a and which may have pairwise overlaps of integer length from 1 to a. We prove that the number of pyramids of size m, i.e. consisting of m pieces, equals (am-1,m-1) for each a >= 2. This generalises a well known result for a = 2. A bijective correspondence between so-called right (or left) pyramids and a-ary trees is pointed out, and it is shown that asymptotically the average width of pyramids is proportional to the square root of the size.
M3 - Working paper
BT - Enumeration of pyramids of one-dimensional pieces of arbitrary fixed integer length
PB - Museum Tusculanum
ER -
ID: 16094367