Q catalan numbers
WebThe q-Catalan numbers are manifestly q- P-recursive (if I can put it like that). $\endgroup$ – Bruce Westbury. May 4, 2010 at 20:59 $\begingroup$ In any case, the equation will not be small. I looked for both q-differential equations and q-recurrences using the first 100 coefficients, and found nothing. So it's probably fair to conjecture ... WebSep 7, 2000 · Displayed below are the polynomials C_ {n} (q,t) for n=2 through n=6 . For convenience, the coefficients have been arranged into an array: the coefficient of q^ {h}t^ …
Q catalan numbers
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WebThe 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 … WebOct 15, 2015 · $\begingroup$ We went over Catalan number related puzzles, but no examples like the ones above, and yes we were presented with that formula. $\endgroup$ – D.Peterson Oct 14, 2015 at 23:05
WebJul 12, 2024 · Definition: Catalan Number The n th Catalan number, C n, is the number of different ways in which brackets can be put around n terms, to indicate different orders of combining the terms. Thus, for example, C 3 = 2, since three terms can be combined as either [ (_·_) ·_], or [_·_ (_·_)]. WebThe rational Catalan numbers Cat ( a / b; q) are defined as. Cat ( a / b; q) = 1 [ a + b] q [ a + b a] q. This is a q -analog of the number of paths from ( 0, 0) to ( b, a) staying weakly above …
WebApr 26, 2008 · The q -Catalan numbers studied by Carlitz and Riordan are polynomials in q with nonnegative coefficients. They evaluate, at q = 1, to the Catalan numbers: 1, 1, 2, 5, …
WebJun 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.
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 … determine acv of a used carWebThe Catalan numbers are a sequence of positive integers that appear in many counting problems in combinatorics. They count certain types of lattice paths, permutations, binary … chunky long necklaces for women ukWebMay 27, 2024 · The -Catalan numbers and their rational analogues are special cases of this construction. In this paper, we give a purely combinatorial treatment of these polynomials and show that in many cases they have nonnegative integer coefficients. determine acv of homeWebViewed 2k times. 5. 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: C n … determine address by latitude and longitudeWebNov 25, 2015 · These parking functions, which are counted by b a−1, carry a permutation representation of S a in which the number of orbits is the “rational” Catalan number {\frac {1} {a+b} \left ( \begin {array} {ll} a+b \\ a \end {array} \right)}. First, we compute the Frobenius characteristic of the S a -module of ( a, b )-parking functions, giving ... chunky long floating shelvesWebSep 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 determine a function’s intervals of concavityWebJun 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 $t=1$. chunkyloversean