Enumeration of pyramids of one-dimensional pieces of arbitrary fixed integer length

Publikation: Working paperForskning

Standard

Enumeration of pyramids of one-dimensional pieces of arbitrary fixed integer length. / Durhuus, Bergfinnur; Eilers, Søren.

Museum Tusculanum, 2009.

Publikation: Working paperForskning

Harvard

Durhuus, B & Eilers, S 2009 'Enumeration of pyramids of one-dimensional pieces of arbitrary fixed integer length' Museum Tusculanum.

APA

Durhuus, B., & Eilers, S. (2009). Enumeration of pyramids of one-dimensional pieces of arbitrary fixed integer length. Museum Tusculanum.

Vancouver

Durhuus B, Eilers S. Enumeration of pyramids of one-dimensional pieces of arbitrary fixed integer length. Museum Tusculanum. 2009.

Author

Durhuus, Bergfinnur ; Eilers, Søren. / Enumeration of pyramids of one-dimensional pieces of arbitrary fixed integer length. Museum Tusculanum, 2009.

Bibtex

@techreport{0063e9d0e03511deba73000ea68e967b,
title = "Enumeration of pyramids of one-dimensional pieces of arbitrary fixed integer length",
abstract = "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.",
author = "Bergfinnur Durhuus and S{\o}ren Eilers",
note = "Keywords: math.CO; 05A15; 82B41",
year = "2009",
language = "English",
publisher = "Museum Tusculanum",
type = "WorkingPaper",
institution = "Museum Tusculanum",

}

RIS

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