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Selections Without Adjacency on a Rectangular Grid - MaRDI portal

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Selections Without Adjacency on a Rectangular Grid

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Publication:6254615

arXiv1409.3869MaRDI QIDQ6254615

Author name not available (Why is that?)

Publication date: 12 September 2014

Abstract: Using T(m,n;k) to denote the number of ways to make a selection of k squares from an (m x n) rectangular grid with no two squares in the selection adjacent, we give a formula for T(2,n;k), prove some identities satisfied by these numbers, and show that T(2,n;k) is given by a degree k polynomial in n. We give simple formulas for the first few (most significant) coefficients of the polynomials. We give corresponding results for T(3,n;k) as well. Finally we prove a unimodality theorem which shows, in particular, how to choose k in order to maximize T(2,n;k).





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