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1.
《Discrete Mathematics》2022,345(7):112898
The Hamming distance between two equal-length words u, v is the number of positions where u and v differ. The words u and v are said to be conjugates if there exist non-empty words such that and . The smallest value can take on is 0, when x and y commute. But, interestingly, the next smallest value can take on is 2 and not 1. In this paper, we consider conjugates and where . More specifically, we provide an efficient formula to count the number of length-n words over a k-letter alphabet that have a conjugate such that . We also provide efficient formulae for other quantities closely related to . Finally, we show that grows erratically: cubically for n prime, but exponentially for n even. 相似文献
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The authors establish the boundedness of the variation operators associated with the heat semigroup, Riesz transforms and commutators generated by the Riesz transforms and BMO-type functions in the Schrödinger setting on the Morrey spaces. 相似文献
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A 3‐phase Barker array is a matrix of third roots of unity for which all out‐of‐phase aperiodic autocorrelations have magnitude 0 or 1. The only known truly two‐dimensional 3‐phase Barker arrays have size 2 × 2 or 3 × 3. We use a mixture of combinatorial arguments and algebraic number theory to establish severe restrictions on the size of a 3‐phase Barker array when at least one of its dimensions is divisible by 3. In particular, there exists a double‐exponentially growing arithmetic function T such that no 3‐phase Barker array of size with exists for all . For example, , , and . When both dimensions are divisible by 3, the existence problem is settled completely: if a 3‐phase Barker array of size exists, then . 相似文献
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借助半群的Malcev积和公理化条件,对超富足半群及其子类进行了刻画,给出了超富足半群及其子类的若干特征. 相似文献
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Joachim Reineke 《代数通讯》2013,41(2):649-660
We consider several different theories of commutative rings with a new predicate symbol | together with the additional axiom a|b ? ?c (a . c = b) and show that none of these has a model companion. 相似文献
9.
Richard Varro 《代数通讯》2013,41(7):2426-2448
We give the identities generating the spaces of degree 4 multilinear identities satisfied by the non commutative 0th-order Bernstein algebras and the non commutative mutation algebras. For it, we use a method reducing the search for multilinear identities to the resolution of linear systems. 相似文献
10.
Affine semigroups are convex sets on which there exists an associative binary operation which is affine separately in either variable. They were introduced by Cohen and Collins in 1959. We look at examples of affine semigroups which are of interest to matrix and operator theory and we prove some new results on the extreme points and the absorbing elements of certain types of affine semigroups. Most notably we improve a result of Wendel that every invertible element in a compact affine semigroup is extreme by extending this result to linearly bounded affine semigroups. 相似文献