Covering a chessboard with staircase walks

Eyal Ackerman; Rom Pinchasi

doi:10.1016/j.disc.2013.07.017

Covering a chessboard with staircase walks

Eyal Ackerman, Rom Pinchasi

Faculty of Natural Sciences

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

Abstract

An ascending (resp., descending) staircase walk on a chessboard is a rook's path that goes either right or up (resp., down) in each step. We show that the minimum number of staircase walks that together visit every square of an n×n chessboard is ⌉2/3⌉.

Original language	English
Pages (from-to)	2547-2551
Number of pages	5
Journal	Discrete Mathematics
Volume	313
Issue number	22
DOIs	https://doi.org/10.1016/j.disc.2013.07.017
State	Published - 2013

Bibliographical note

Funding Information:
The second author was supported by a BSF grant (grant No. 2008290 ) and by an ISF grant (grant No. 1357/12 ).

Keywords

Lattice path
Staircase walk

ASJC Scopus subject areas

Theoretical Computer Science
Discrete Mathematics and Combinatorics

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10.1016/j.disc.2013.07.017

Cite this

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title = "Covering a chessboard with staircase walks",

abstract = "An ascending (resp., descending) staircase walk on a chessboard is a rook's path that goes either right or up (resp., down) in each step. We show that the minimum number of staircase walks that together visit every square of an n×n chessboard is ⌉2/3⌉.",

keywords = "Lattice path, Staircase walk",

author = "Eyal Ackerman and Rom Pinchasi",

note = "Funding Information: The second author was supported by a BSF grant (grant No. 2008290 ) and by an ISF grant (grant No. 1357/12 ).",

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AU - Pinchasi, Rom

N1 - Funding Information: The second author was supported by a BSF grant (grant No. 2008290 ) and by an ISF grant (grant No. 1357/12 ).

PY - 2013

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N2 - An ascending (resp., descending) staircase walk on a chessboard is a rook's path that goes either right or up (resp., down) in each step. We show that the minimum number of staircase walks that together visit every square of an n×n chessboard is ⌉2/3⌉.

AB - An ascending (resp., descending) staircase walk on a chessboard is a rook's path that goes either right or up (resp., down) in each step. We show that the minimum number of staircase walks that together visit every square of an n×n chessboard is ⌉2/3⌉.

KW - Lattice path

KW - Staircase walk

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U2 - 10.1016/j.disc.2013.07.017

DO - 10.1016/j.disc.2013.07.017

M3 - Article

AN - SCOPUS:84883039857

SN - 0012-365X

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EP - 2551

JO - Discrete Mathematics

JF - Discrete Mathematics

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Covering a chessboard with staircase walks

Abstract

Bibliographical note

Keywords

ASJC Scopus subject areas

Access to Document

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