LP-decodable multipermutation codes

In this paper, we introduce a new way of constructing and decoding multipermutation codes. Multipermutations are permutations of a multiset that may consist of duplicate entries. We first introduce a new class of matrices called multipermutation matrices. We characterize the convex hull of multipermutation matrices. Based on this characterization, we propose a new class of codes that we term LP-decodable multipermutation codes. Then, we derive two LP decoding algorithms. We first formulate an LP decoding problem for memoryless channels. We then derive an LP algorithm that minimizes the Chebyshev distance. Finally, we show a numerical example of our algorithm.Comment: This work was supported by NSF and NSERC. To appear at the 2014 Allerton Conferenc

Twins in words and long common subsequences in permutations

A large family of words must contain two words that are similar. We investigate several problems where the measure of similarity is the length of a common subsequence. We construct a family of n^{1/3} permutations on n letters, such that LCS of any two of them is only cn^{1/3}, improving a construction of Beame, Blais, and Huynh-Ngoc. We relate the problem of constructing many permutations with small LCS to the twin word problem of Axenovich, Person and Puzynina. In particular, we show that every word of length n over a k-letter alphabet contains two disjoint equal subsequences of length cnk^{-2/3}. Many problems are left open.Comment: 18+epsilon page

An Inhomogeneous Multispecies TASEP on a Ring

We reinterpret and generalize conjectures of Lam and Williams as statements about the stationary distribution of a multispecies exclusion process on the ring. The central objects in our study are the multiline queues of Ferrari and Martin. We make some progress on some of the conjectures in different directions. First, we prove their conjectures in two special cases by generalizing the rates of the Ferrari-Martin transitions. Secondly, we define a new process on multiline queues, which have a certain minimality property. This gives another proof for one of the special cases; namely arbitrary jump rates for three species.Comment: 21 pages, 1 figure. major changes in exposition; definitions clarified and terminology made more self-containe

Semigroups of tolerance relations

AbstractWe give an abstract algebraic characterization of semigroups of tolerance relations and semigroups of symmetric binary relations