The Frequency of Summands of a Particular Size in Palindromic Compositions

نویسندگان

  • Phyllis Chinn
  • Ralph Grimaldi
  • Silvia Heubach
چکیده

A composition of a positive integer n consists of an ordered sequence of positive integers whose sum is n. A palindromic composition is one for which the sequence is the same from left to right as from right to left. This paper shows various ways of generating all palindromic compositions, counts the number of times each integer appears as a summand among all the palindromic compositions of n, and describes several patterns among the numbers generated in the process of enumeration.

برای دانلود رایگان متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

ثبت نام

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

منابع مشابه

Compositions of N with No Occurrence of K

A composition of n is an ordered collection of one or more positive integers whose sum is n. The number of summands is called the number of parts of the composition. A palindromic composition or palindrome is a composition in which the summands are the same in the given or in reverse order. Compositions may be viewed as tilings of 1-by-n rectangles with 1-by-i rectangles, 1 i n ≤ ≤ . We count t...

متن کامل

Counting Rises, Levels, and Drops in Compositions

A composition of n ∈ N is an ordered collection of one or more positive integers whose sum is n. The number of summands is called the number of parts of the composition. A palindromic composition of n is a composition of n in which the summands are the same in the given or in reverse order. In this paper we study the generating function for the number of compositions (respectively, palindromic ...

متن کامل

COMPOSITIONS OF n WITH PARTS IN A SET

Let A be any set of positive integers and n ∈ N. A composition of n with parts in A is an ordered collection of one or more elements in A whose sum is n. A palindromic composition of n with parts in A is a composition of n with parts in A in which the summands are the same in the given or in reverse order. A Carlitz (palindromic) composition of n with parts in A is a (palindromic) composition o...

متن کامل

( 1 , k ) - Compositions

A (1, k)-composition of a positive integer n consists of an ordered sequence of the integers 1 and k whose sum is n. A palindromic (1, k)-composition is one for which the sequence is the same from left to right as from right to left. We give recursive equations and generating functions for the total number of such compositions and palindromes, and for the number of 1’s, k’s, “+”signs and summan...

متن کامل

High- and Mid-Frequency Vocabulary Size as Predictors of Iranian University EFL Students’ Speaking Performance

Literature is replete with the studies focusing on the role of vocabulary knowledge in second language receptive skills. However, the relationship between the aspects of vocabulary knowledge and productive skills in general, and the speaking performance in particular has remained scanty in the related literature. This paper examined the relationship between knowledge of L2 vocabulary size at di...

متن کامل

ذخیره در منابع من


  با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید

عنوان ژورنال:
  • Ars Comb.

دوره 69  شماره 

صفحات  -

تاریخ انتشار 2003