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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On the Congruences of Some Combinatorial Numbers
TL;DR: In this paper, the authors apply Lucas' theorem to evaluate the congruences of several combinatorial numbers, including the central Delannoy numbers and a class of Apery-like numbers.
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On the Parity of Certain Coefficients for a $q$-Analogue of the Catalan Numbers
TL;DR: This paper shows how one can characterize the charge-Wilf equivalence classes for subsets of $S_3$ and uses a bijection between the charge statistic and the major index to prove a conjecture of Dokos, Dwyer, Johnson, Sagan and Selsor regarding powers of 2 and theMajor index.
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A combinatorial approach to the power of 2 in the number of involutions
Dongsu Kim,Jang Soo Kim +1 more
TL;DR: This work provides a combinatorial approach to the largest power of p in the number of permutations @p with @p^p=1, for a fixed prime number p, and finds the largestPower of 2 in theNumber of involutions, in the signed sum of involuntaryutions and in the numbers of even or odd involutions.
Posted Content
Inversion polynomials for 321-avoiding permutations
TL;DR: A generalization of a conjecture giving a recursion for the inversion polynomial of 321-avoiding permutations is proved, giving a Recursion of Dokos, Dwyer, Johnson, Sagan, and Selsor's conjecture.
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Thin Sets with Fat Shadows: Projections of Cantor Sets
Franklin Mendivil,Tara Taylor +1 more
TL;DR: In this note, a simple construction of a Cantor subset of the unit square whose projection in every direction is a line segment is given, which can easily be generalized to n dimensions.
References
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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.