STATISTICS of DOMINO TILINGS on A RECTANGULAR BOARD

Thotsaporn Aek Thanatipanonda

STATISTICS of DOMINO TILINGS on A RECTANGULAR BOARD

Thotsaporn Aek Thanatipanonda

Science Division

Research output: Contribution to journal › Article › peer-review

Abstract

It is well-known that the Fibonacci sequence, Fn, is the number of ways to cover a 2-by-(n−1) board using only horizontal (H) or vertical (V) 2-by-1 dominoes. The number of ways to tile a rectangular m-by-n board by these dominoes was given in 1961 by Kasteleyn through the evaluation of a determinant. In this paper, we apply an automated method for the mixed moments E[V^aH^b] for fixed non-negative integers a,b on a general m-by-n board. These moments will give information about the distribution of “V-H statistics”. This is an implementation of the work of Zeilberger.

Original language	English
Pages (from-to)	145-153
Number of pages	9
Journal	Fibonacci Quarterly
Volume	57
Issue number	5
Publication status	Published - Dec 2019

Cite this

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abstract = "It is well-known that the Fibonacci sequence, Fn, is the number of ways to cover a 2-by-(n−1) board using only horizontal (H) or vertical (V) 2-by-1 dominoes. The number of ways to tile a rectangular m-by-n board by these dominoes was given in 1961 by Kasteleyn through the evaluation of a determinant. In this paper, we apply an automated method for the mixed moments E[VaHb] for fixed non-negative integers a,b on a general m-by-n board. These moments will give information about the distribution of “V-H statistics”. This is an implementation of the work of Zeilberger.",

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STATISTICS of DOMINO TILINGS on A RECTANGULAR BOARD

Abstract

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