Matrices uniquely determined by their lonesums
SCIE
SCOPUS
- Title
- Matrices uniquely determined by their lonesums
- Authors
- Kim, HK; Krotov, DS; Lee, JY
- Date Issued
- 2013-04-01
- Publisher
- Sciencedirect
- Abstract
- A matrix is lonesum if it can be uniquely reconstructed from its row and column sums. Brewbaker computed the number of m x n binary lonesum matrices. Kaneko defined the poly-Bernoulli numbers of an integer index, and showed that the number of m x n binary lonesum matrices is equal to the mth poly-Bernoulli number of index -n. In this paper, we are interested in q-ary lonesum matrices. There are two types of lonesumness for q-ary matrices, namely strongly and weakly lonesum. We first study strongly lonesum matrices: We compute the number of m x n q-ary strongly lonesum matrices, and provide a generalization of Kaneko's formulas by deriving the generating function for the number of m x n q-ary strongly lonesum matrices. Next, we study weakly lonesum matrices: We show that the number of forbidden patterns for q-ary weakly lonesum matrices is infinite if q >= 5, and construct some forbidden patterns for q = 3, 4. We also suggest an open problem related to ternary and quaternary weakly lonesum matrices. (C) 2012 Elsevier Inc. All rights reserved.
- Keywords
- Poly-Bernoulli numbers; Lonesum matrices; q-Ary matrices; Forbidden patterns; Strongly lonesum matrices; Weakly lonesum matrices; POLY-BERNOULLI NUMBERS; QUANTUM MATRICES; CLOSED FORMULA; H-PRIMES
- URI
- https://oasis.postech.ac.kr/handle/2014.oak/15719
- DOI
- 10.1016/J.LAA.2012.11.027
- ISSN
- 0024-3795
- Article Type
- Article
- Citation
- Linear Algebra and its Applications, vol. 438, no. 7, page. 3107 - 3123, 2013-04-01
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