Mintys.Catalan istorijaPaslėpti nežymius pakeitimus - Rodyti kodo pakeitimus 2017 rugsėjo 20 d., 20:33
atliko -
Pakeistos 1-67 eilutės iš
Žr. Matematika? Consider how to relate the Catalan generating function to a complex number and a context-free grammar. How does binary tree height correspond to the difference between left-right parentheses? Look at q-catalan numbers. How do they relate to parentheses discrepancy? What are the q-t-catalan numbers, what do they count, and how do they relate to the Macdonald polynomials? Consider how to relate the boundedness of the generating function to the idea that there is a finite mismatch between left and right parentheses, whereas if the number of left parentheses grows without bound, then the function diverges to infinity. Consider what we know about the boundedness of the generating function in the complex plane. Dievas: walks on binary trees (C,I,U). Ar tai tas pats kaip "ordered binary trees"? Ar juos skaičiuoja Catalan skaičiai?
Jeigu pridėti c + d (delta) ką sužinotumėme apie mažą paklaidą? The issue of memory required by automata - that this is "explicit" truth needed to supplement "implicit" truth. Analytic Combinatorics by Philippe Flajolet, Robert Sedgewick, 2009. They briefly mention the connection between Mandelbrot sets and Catalan numbers as noting "the speed of convergence" for "the generating functions of binary trees of bounded height". Look for Catalan numbers:
|z| ≤ r < 1/4, simple majorant series considerations show that the convergence yh(z)→y(z) is uniformly geometric. When z ≥ s > 1/4 it can be checked that the yh(z) grow doubly exponentially. What happens in-between, in a delta–domain, needs to be quantified. We do so following Flajolet, Gao, Odlyzko, and Richmond [230, 246]. (They analyze the convergence in the interesting domain.)
It seems that the Catalan numbers serve to count both of these cases:
Whereas "all binary trees" (all parentheses) are given by binomial theorem, as can be seen by expanding ( + ) to the N. Mandelbrot set rule: The simplest "mixing rule": "Add the input (complex vector c), add the output ("multiply by 2" by complex rotating and squaring)." The $q,t$-Catalan Numbers and the Space of Diagonal Harmonics (University Lecture Series) by James Haglund. With an appendix on the MacDonald polynomials (linked to root weights). Square root as a sign of "dual" mid-point (reflection point) in a duality.
į:
2016 birželio 09 d., 16:54
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Pridėtos 19-20 eilutės:
Jeigu pridėti c + d (delta) ką sužinotumėme apie mažą paklaidą? 2016 gegužės 16 d., 15:52
atliko -
Pridėta 18 eilutė:
2016 gegužės 16 d., 15:26
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Pridėtos 17-18 eilutės:
Dievas: walks on binary trees (C,I,U). Ar tai tas pats kaip "ordered binary trees"? Ar juos skaičiuoja Catalan skaičiai? Pakeista 64 eilutė iš:
į:
2016 gegužės 16 d., 14:40
atliko -
Pridėtos 7-12 eilutės:
How does binary tree height correspond to the difference between left-right parentheses? Look at q-catalan numbers. How do they relate to parentheses discrepancy? What are the q-t-catalan numbers, what do they count, and how do they relate to the Macdonald polynomials? Ištrintos 13-14 eilutės:
Look at q-catalan numbers. 2016 gegužės 16 d., 14:36
atliko -
Pridėtos 44-50 eilutės:
It seems that the Catalan numbers serve to count both of these cases:
Whereas "all binary trees" (all parentheses) are given by binomial theorem, as can be seen by expanding ( + ) to the N. Mandelbrot set rule: The simplest "mixing rule": "Add the input (complex vector c), add the output ("multiply by 2" by complex rotating and squaring)." 2016 gegužės 16 d., 14:16
atliko -
Pakeista 36 eilutė iš:
it can be checked that the yh(z) growdoubly exponentially. What happens in-between, in a delta–domain, needs to be quantified. We do so following Flajolet, Gao, Odlyzko, and Richmond [230, 246]. į:
it can be checked that the yh(z) grow doubly exponentially. What happens in-between, in a delta–domain, needs to be quantified. We do so following Flajolet, Gao, Odlyzko, and Richmond [230, 246]. (They analyze the convergence in the interesting domain.) 2016 gegužės 16 d., 14:15
atliko -
Pakeistos 23-24 eilutės iš
tractable model of a coalescence-fragmentation process, which is of great interest in several areas of science, for which we refer to Aldous’ survey [9]." į:
2016 gegužės 16 d., 14:12
atliko -
Pakeistos 38-39 eilutės iš
į:
Pridėtos 47-48 eilutės:
Square root as a sign of "dual" mid-point (reflection point) in a duality. 2016 gegužės 16 d., 14:02
atliko -
Pakeistos 31-37 eilutės iš
į:
|z| ≤ r < 1/4, simple majorant series considerations show that the convergence yh(z)→y(z) is uniformly geometric. When z ≥ s > 1/4 it can be checked that the yh(z) growdoubly exponentially. What happens in-between, in a delta–domain, needs to be quantified. We do so following Flajolet, Gao, Odlyzko, and Richmond [230, 246]. 2016 gegužės 16 d., 13:59
atliko -
Pridėtos 30-31 eilutės:
2016 gegužės 16 d., 13:55
atliko -
Pakeistos 27-29 eilutės iš
į:
2016 gegužės 16 d., 13:49
atliko - 2016 gegužės 16 d., 13:49
atliko -
Pridėtos 25-26 eilutės:
2016 gegužės 16 d., 13:47
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Pakeistos 18-19 eilutės iš
į:
Pakeistos 22-23 eilutės iš
The $q,t$-Catalan Numbers and the Space of Diagonal Harmonics (University Lecture Series) by James Haglund. With an appendix on the MacDonald polynomials. į:
tractable model of a coalescence-fragmentation process, which is of great interest in several areas of science, for which we refer to Aldous’ survey [9]." The $q,t$-Catalan Numbers and the Space of Diagonal Harmonics (University Lecture Series) by James Haglund. With an appendix on the MacDonald polynomials (linked to root weights). 2016 gegužės 16 d., 13:37
atliko -
Pridėtos 14-20 eilutės:
The issue of memory required by automata - that this is "explicit" truth needed to supplement "implicit" truth. Analytic Combinatorics by Philippe Flajolet, Robert Sedgewick, 2009. They briefly mention the connection between Mandelbrot sets and Catalan numbers as noting "the speed of convergence" for "the generating functions of binary trees of bounded height". Look for Catalan numbers:
2016 gegužės 16 d., 12:58
atliko -
Pridėtos 12-13 eilutės:
The $q,t$-Catalan Numbers and the Space of Diagonal Harmonics (University Lecture Series) by James Haglund. With an appendix on the MacDonald polynomials. 2016 gegužės 16 d., 10:58
atliko -
Pridėtos 1-15 eilutės:
Consider how to relate the Catalan generating function to a complex number and a context-free grammar. Consider how to relate the boundedness of the generating function to the idea that there is a finite mismatch between left and right parentheses, whereas if the number of left parentheses grows without bound, then the function diverges to infinity. Look at q-catalan numbers. Consider what we know about the boundedness of the generating function in the complex plane.
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Puslapis paskutinį kartą pakeistas 2017 rugsėjo 20 d., 20:33
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