THE SITE-PERIMETER OF WORDS

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BLECHER AUBREY; BRENNAN CHARLOTTE; KNOPFMACHER ARNOLD; MANSOUR TOUFLK

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Journal: TRANSACTIONS ON COMBINATORICS Year:2017 | Volume:6 | Issue:2 Page(s): 37-48

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Information Journal Paper

Title

THE SITE-PERIMETER OF WORDS

Author(s)

BLECHER AUBREY | BRENNAN CHARLOTTE | KNOPFMACHER ARNOLD | MANSOUR TOUFLK | Issue Writer Certificate

Keywords

WORDS

BARGRAPHS

SITE-PERIMETER

GENERATING FUNCTIONS

Abstract

We define [k] ={1, 2, 3,…, k} to be a (totally ordered) alphabet on k letters. A word wof length n on the alphabet [k] is an element of [k] n. A word can be represented by a bargraph which is a family of column-convex polyominoes whose lower edge lies on the x -axis and in which the height of the i -th column in the bargraph equals the size of the i -th part of the word. Thus these BARGRAPHS have heights which are less than or equal to k. We consider the SITE-PERIMETER, which is the number of nearest-neighbour cells outside the boundary of the polyomino. The generating function that counts the SITE-PERIMETER of WORDS is obtained explicitly. From a functional equation we find the average SITE-PERIMETER of WORDS of length n over the alphabet [k]. We also show how these statistics may be obtained using a direct counting method and obtain the minimum and maximum values of the SITE-PERIMETERs.

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APA: Copy

BLECHER, AUBREY, BRENNAN, CHARLOTTE, KNOPFMACHER, ARNOLD, & MANSOUR, TOUFLK. (2017). THE SITE-PERIMETER OF WORDS. TRANSACTIONS ON COMBINATORICS, 6(2), 37-48. SID. https://sid.ir/paper/714595/en

Vancouver: Copy

BLECHER AUBREY, BRENNAN CHARLOTTE, KNOPFMACHER ARNOLD, MANSOUR TOUFLK. THE SITE-PERIMETER OF WORDS. TRANSACTIONS ON COMBINATORICS[Internet]. 2017;6(2):37-48. Available from: https://sid.ir/paper/714595/en

IEEE: Copy

AUBREY BLECHER, CHARLOTTE BRENNAN, ARNOLD KNOPFMACHER, and TOUFLK MANSOUR, “THE SITE-PERIMETER OF WORDS,” TRANSACTIONS ON COMBINATORICS, vol. 6, no. 2, pp. 37–48, 2017, [Online]. Available: https://sid.ir/paper/714595/en

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