Results 51 to 60 of about 56,637 (162)
Permutations avoiding an increasing number of length-increasing forbidden subsequences [PDF]
Discrete Mathematics & Theoretical Computer Science, 2000 A permutation π is said to be τ -avoiding if it does not contain any subsequence having all the same pairwise comparisons as τ . This paper concerns the characterization and enumeration of permutations which avoid a set F^j of subsequences increasing ...
Elena Barcucci +3 more
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Journal of Combinatorial Theory, Series A, 1985 Let \(C_ n\) be the set of Catalan words: binary words with n zeros and n ones such that each initial segment has at least as many zeros and ones. For \(w\in C_ n\), let d(w) be the number of descents, a(w) be the sum over all descents of the number of zeros to the left, b(w) be the sum over all descents of the number of ones to the left.
Fürlinger, J, Hofbauer, J
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Catalan pairs and Fishburn triples
, 2015 Disanto, Ferrari, Pinzani and Rinaldi have introduced the concept of 'Catalan pair', which is a pair of partial orders (S,R) satisfying certain axioms.
Jelínek, Vít
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Growing and Destroying Catalan-Stanley Trees [PDF]
Discrete Mathematics & Theoretical Computer Science, 2018 Stanley lists the class of Dyck paths where all returns to the axis are of odd length as one of the many objects enumerated by (shifted) Catalan numbers.
Benjamin Hackl, Helmut Prodinger
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A combinatorial identity with application to Catalan numbers
, 2005 By a very simple argument, we prove that if $l,m,n$ are nonnegative integers then $$\sum_{k=0}^l(-1)^{m-k}\binom{l}{k}\binom{m-k}{n}\binom{2k}{k-2l+m} =\sum_{k=0}^l\binom{l}{k}\binom{2k}{n}\binom{n-l}{m+n-3k-l}.
Pan, Hao, Sun, Zhi-Wei
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Success Run Waiting Times and Fuss-Catalan Numbers
Journal of Probability and Statistics, 2015 We present power series expressions for all the roots of the auxiliary equation of the recurrence relation for the distribution of the waiting time for the first run of k consecutive successes in a sequence of independent Bernoulli trials, that is, the ...
S. J. Dilworth, S. R. Mane
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On generalized bihyperbolic Mersenne numbers [PDF]
Mathematica BohemicaIn this paper, a new generalization of Mersenne bihyperbolic numbers is introduced. Some of the properties of presented numbers are given. A general bilinear index-reduction formula for the generalized bihyperbolic Mersenne numbers is obtained.
Dorota Bród, Anetta Szynal-Liana
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Some Identities on the Twisted q-Analogues of Catalan-Daehee Numbers and Polynomials
Axioms, 2021 In this paper, the author considers twisted q-analogues of Catalan-Daehee numbers and polynomials by using p-adic q-integral on Zp. We derive some explicit identities for those twisted numbers and polynomials related to various special numbers and ...
Dongkyu Lim
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Harmonic numbers, Catalan's triangle and mesh patterns
, 2012 The notion of a mesh pattern was introduced recently, but it has already proved to be a useful tool for description purposes related to sets of permutations. In this paper we study eight mesh patterns of small lengths. In particular, we link avoidance of
Kitaev, Sergey, Liese, Jeffrey
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On generalised catalan numbers
Discrete Mathematics, 1978 AbstractThe Catalan number Cn is defined to be 2nn(n+1). One of its occurrences is as the number of ways of bracketing a product of n+1 terms taken from a set with binary operation. In this note the corresponding result for a set with a k-ary operation is considered.
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