2014/09/12 by Jacob A. Siehler, Jacob Siehler, Siehler, Jacob A.
Computer Science · Engineering · Mathematics · #05A15 #Advanced Data Compression Techniques #Algorithms and Data Compression #Combinatorics (math.CO) #FOS: Mathematics #graph theory and CDMA systems #math.CO #msc:05A15
paper · pdf · doi:10.48550/arxiv.1409.3869
arxiv created 2014/09/12 · openalex publication_date 2014/09/12 · arxiv updated 2014/09/16 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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).