Q catalan numbers
Web1.1. Rational q;t-Catalan numbers. Let aand bbe coprime positive integers. The ra-tional q;t-Catalan number C a;b(q;t) 2N[q;t] was introduced by Loehr{Warrington [LW09] (see also … WebThree experimental studies are presented testing the choice of a left or a right dislocation in Catalan, depending on the bridging relation between the dislocate and its antecedent. We make the hypothesis that the stronger the anaphoric link between the dislocate and its antecedent, the more appropriate a right dislocation is, whereas the opposite is true for …
Q catalan numbers
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WebThe q, t-Catalan numbers arise naturally in the study of diagonal harmonics. They are conjectured to be the coefficient of the sign representation in the Frobenius series for the … WebAug 30, 2024 · Recursions for rational q,t-Catalan numbers. We give a simple recursion labeled by binary sequences which computes rational -Catalan power series, both in …
Webi.e., the q-Catalan numbers C,(q) converge to the partition function. For the c,,(q) the exponent of q counts the area between the paths of w and of 0101 . ..Ol. (I-CATALAN NUMBERS 253 Another combinatorial model for Catalan numbers is described in Knuth [ 15, p. 238f, Exs. 2-51; he considers a stack where at each of 2n steps either ... WebJun 5, 2015 · The $q$-Catalan you mentioned comes from the formula $$q^ { (a-1) (b-1)/2}\mathrm {Cat}_ {a,b} (q,q^ {-1})=\frac {1} { [a+b]_q} { a+b \brack a}_q$$ by setting $ (a,b)= (n,n+1)$ and the "other" $q$-Catalan number comes from setting $t=1$.
WebCatalan words ˙ qmaj(˙) = 1 (n+1)q 2n n q: The Carlitz-Riordan q-Catalan Let Dn denote the set of Catalan paths, and set Cn(q)= X ˙2Dn qarea(˙) where area(˙)isthenumberof … Webq;t-Catalan numbers q;t-Catalan numbers: examples Another interesting degeneration: c n(q;1) is a sum over all Dyck paths weighted by the area between a path and the diagonal: …
Web%i %s 1,1,6,161,20466,12833546,40130703276,627122621447281, %t 48995209411107768186,19138851672289046707772366, %u …
WebViewed 707 times. 8. I had completed a paper describing the q -Catalan numbers, which is the q -analog of the Catalan numbers. The n -th Catalan numbers can be represented by: … tart testoWebMay 16, 2024 · Clearly \lim _ {q\rightarrow 1}C_n (q)=C_n. C_n (q) is often called the Carlitz–Riordan q -Catalan number. The Carlitz–Riordan q -Catalan numbers also have … tart thesisWebSep 19, 2007 · Catalan numbers and the generalized q -Catalan numbers are normal. Despite the fact that these coefficients are not unimodal for small n, we conjecture that for sufficiently large n, the... tartt fiction awardWebMay 5, 2024 · I would like to know if the following recurrence relation for Catalan numbers (see mathoverflow.net/questions/191524 and also math.stackexchange.com/questions/2113830) has appeared in a paper or a book, so that I can cite it. C n = 1 + ∑ k = 1 ⌈ n 2 ⌉ ( − 1) k + 1 ( n − k k) C n − k where C n is the n -th … tart testWebSep 7, 2000 · The qt-Catalan numbers Definition of the (q,t)-Catalan numbers Tables of q,t-Catalan numbers in postscript form Maple programs for computing the q,t-Catalan numbers The connection with the operator Nabla (NEW! Sept 7, 2000): A combinatorial interpretation for this sequence the bridge story donna shopperWebThe q −Narayana numbers are polynomials in q with integer coefficients. The first values of these q −Narayana numbers are given in the following table: 1 q1 q3 2q+q2 1 q6 q2 +2q3 … tart the movieWebJun 11, 2024 · Further q -analogues of the Catalan numbers and related formulae can be found in (Andrews 2010, 2011; Carlitz and Riordan 1964; Chu 2024; Fürlinger and Hofbauer 1985; Jin and Nebel 2015 ). Recently, the second author (Chu 2024, Theorem 1) found a common generalization of the above three identities. tart the movie cast