Embedding a Latin square with transversal into a projective space
نویسندگان
چکیده
Article history: Received 20 May 2010 Available online xxxx
منابع مشابه
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A latin transversal in a square matrix of order n is a set of entries, no two in the same row or column, which are pairwise distinct. A longstanding conjecture of Ryser states that every Latin square with odd order has a latin transversal. Some results on the existence of a large partial latin transversal can be found in [11,6,16]. Mainly motivated by Ryser’s conjecture, Erdős and Spencer [8] p...
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A k-plex in a latin square of order n is a selection of kn entries that includes k representatives from each row and column and k occurrences of each symbol. A 1-plex is also known as a transversal. It is well known that if n is even then Bn, the addition table for the integers modulo n, possesses no transversals. We show that there are a great many latin squares that are similar to Bn and have...
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A latin square is a bachelor square if it does not possess an orthogonal mate; equivalently, it does not have a decomposition into disjoint transversals. We define a latin square to be a confirmed bachelor square if it contains an entry through which there is no transversal. We prove the existence of confirmed bachelor squares for all orders greater than three. This resolves the existence quest...
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We suggest and explore a matroidal version of the Brualdi Ryser conjecture about Latin squares. We prove that any n × n matrix, whose rows and Columns are bases of a matroid, has an independent partial transversal of length d2n/3e. We show that for any n, there exists such a matrix with a maximal independent partial transversal of length at most n− 1.
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It is proved that every n×n Latin square has a partial transversal of length at least n−O(log n). The previous papers proving these results [including one by the second author] not only contained an error, but were sloppily written and quite difficult to understand. We have corrected the error and improved the clarity.
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عنوان ژورنال:
- J. Comb. Theory, Ser. A
دوره 118 شماره
صفحات -
تاریخ انتشار 2011