منابع مشابه
Compositions versus Cyclic Compositions
We prove that the sum of greatest common divisors of parts in all compositions of n equals the sum of lengths of all cyclic compositions of n. The proof highlights structural similarities between the set of compositions of n and the set of cyclic compositions of n. 1. Definitions and Statement A composition of the positive integer n is an ordered partition of n; that is, a vector ( ) r p p ...,...
متن کاملMatrix Compositions
In this paper we study the class of m-row matrix compositions (m-compositions, for short), i.e., m-row matrices with nonnegative integer entries in which every column has at least one non-zero element. We provide several enumerative results, various combinatorial identities, and some combinatorial interpretations. Most of these properties are an extension to matrix compositions of the combinato...
متن کاملConcave Compositions
Concave compositions are compositions (i.e. ordered partitions) of a number in which the parts decrease up to the middle summand(s) and increase thereafter. Perhaps the most surprising result is for even length, concave compositions where the generating function turns out to be the quotient of two instances of the pentagonal number theorem with variations of sign. The false theta function disco...
متن کاملReconstructing compositions
We consider the problem of reconstructing compositions of an integer from their subcompositions, which was raised by Raykova (albeit disguised as a question about layered permutations). We show that every composition w of n ≥ 3k+1 can be reconstructed from its set of k-deletions, i.e., the set of all compositions of n− k contained in w. As there are compositions of 3k with the same set of k-del...
متن کاملThe Effect of Selenium, Vitamin E and Copper Injection on the Somatic Cell Count and Milk Compositions in Dairy Cows
Akbar Pirestani,*, Mohammad Javad Bagheri, Sayed Mahdi Hashemi, Amir Hossine Asgarishahi Department of Animal Science, Khorasgan (Isfahan) Branch, Islamic Azad University, Isfahan, Iran *Corresponding author: Email: [email protected] Received: 20 July 2013 Accepted: 21 November 2013 ABSTRACT This study was conducted to evaluate the impact of Se+Vit E and Cu inject...
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ژورنال
عنوان ژورنال: Podzemni radovi
سال: 2016
ISSN: 0354-2904
DOI: 10.5937/podrad1629055c