Combinatorial Properties of Matrices of Zeros and
                        Ones

Ryser, H. J.

doi:10.4153/cjm-1957-044-3

Cited by 525 publications

(312 citation statements)

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“…Graph Theory with Applications This formulation of theorem 11.9 in terms of (0, 1)-matrices is due to Ryser (1957). For other applications of the theory of flows in networks, we refer the reader to Ford and Fulkerson (1962).…”

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confidence: 99%

Graph Theory with Applications

Bondy¹

1976

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confidence: 99%

Graph Theory with Applications

Bondy¹

1976

7,009

3,571

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“…In the context of binary tomography, ghosts first appeared in the reconstruction of binary matrices, under the name of interchanges [21], and later were called switching components [22] or bad configurations. Here it is convenient to represent a digital image as a finite subset of the integer lattice Z 2 .…”

Section: Resultsmentioning

confidence: 99%

Ghosts in Discrete Tomography

et al. 2015

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Switching components, also named bad configurations, interchanges, and ghosts (according to different scenarios) play a key role in the study of ambiguous configurations, which often appear in Discrete Tomography and in several other areas of research. In this paper we give an upper bound for the minimal size bad configurations associated to a given set S of lattice directions. In the special but interesting case of four directions, we show that the general argument can be considerably improved, and we present an algebraic method which provides such an improvement. Moreover, it turns out that finding bad configurations is in fact equivalent to finding multiples of a suitable polynomial in two variables, having only coefficients from the set {−1, 0, 1}. The general problem of describing all polynomials having such multiples seems to be very hard [1]. However, in our particular case, it is hopeful to give some kind of solution. In the context of Digital Image Analysis, it represents an explicit method for the construction of ghosts, and consequently might be

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“…See Lorenz (1949), Kellerer (1961), and Strassen (1965) for a general solution to such problems, which can then be proved to yield Matthews' condition (ii). Gale (1957) and Ryser (1957) deal with the related problem of the existence of matrices with entries 0 or 1 that have given row and column sums; interestingly, the resulting condition can be stated in terms of majorization, the discrete version of second-order stochastic dominance. While this result is restricted to only two agents, it may nevertheless be interesting to explore the connection further.…”

Section: Remarksmentioning

confidence: 99%