Prime and prime power divisibility of Catalan numbers
Ronald Alter,K.K Kubota +1 more
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TLDR
For any prime p, the sequence of Catalan numbers a n = 1 n 2n−2 n−1 is divided by the an prime to p into blocks Bk(k > 0) of an divisible by p, whose lengths and positions are determined.About:
This article is published in Journal of Combinatorial Theory, Series A.The article was published on 1973-11-01 and is currently open access. It has received 52 citations till now. The article focuses on the topics: Prime k-tuple & Almost prime.read more
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Catalan numbers, primes, and twin primes
Christian Aebi,Grant Cairns +1 more
TL;DR: In this paper, einige Beziehungen zwischen Catalan-Zahlen, Primzahlen und Primzahlzwillingen darzustellen, indem nur elementare arithmetische Begriffe angewendet, gleichzeitig aber a also viele (historische) Bezuge fur den an einer weiteren Ausfuhrung interessierten Leser angeboten werden.
Dissertation
Combinatorial enumeration of weighted Catalan numbers
TL;DR: In this article, the authors studied the divisibility property of weighted Catalan and Motzkin numbers and its applications. And they proved the Konvalinka conjecture on the largest power of two dividing weighted Catalan number, when the weight function is a polynomial.
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Congruences for Catalan and Motzkin numbers and related sequences
Emeric Deutsch,Bruce E. Sagan +1 more
TL;DR: This article proved various congruences for the Catalan and Motzkin numbers as well as related sequences in terms of binomial coefficients, including the Thue-Morse sequence, and showed that all these sequences can be expressed as binomial numbers.
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Inversion polynomials for 321-avoiding permutations: addendum
TL;DR: In this article, the inversion number and major index polynomials for permutations of permutations avoiding 321 have been investigated in the context of symmetry, unimodality, behavior modulo 2, and signed enumeration.
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Extreme Palindromes
Kathy Q. Ji,Herbert S. Wilf +1 more
TL;DR: It suffices to show that g − c is concave, since adding a constant to a concave function preserves concavity.
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Historical Note on a Recurrent Combinatorial Problem
TL;DR: Brown as mentioned in this paper presented a historical note on a recurrent combinatorial problem, The American Mathematical Monthly, 72:9, 973-977, DOI: 10.1080/00029890.1965.