Gessel I., Symmetric functions and P-recursiveness. 1990 J. Combin. Theory Ser. A 53 257--285. Home/Search Document Not in Database Summary Related Articles Check |
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Recent Developments in Algebraic Combinatorics - Stanley (2002) (Correct)
....the asymptotic behavior of E(n) We will say only a brief word on the proof of the above results, explaining how combinatorics enters into the picture. Some kind of analytic expression is needed for the distribution of is n (w) Such an expression is provided by the following result of Ira Gessel [26], later proved in other ways by various persons. Theorem. Let u k (n) #fw 2 S n : is n (w) kg U k (x) u k (n) B i (x) 2n i n (n i) Then U k (x) det B ji jj (x) k i;j=1 Example. We have U 2 (x) B 0 (x) B 1 (x) From this it is easy to deduce ....
I. Gessel, Symmetric functions and P-recursiveness, J. Combinatorial Theory (A) 53 (1990), 257-285.
Recent Progress in Algebraic Combinatorics - Stanley (2000) (2 citations) (Correct)
....the asymptotic behavior of E(n) We will say only a brief word on the proof of the above results, explaining how combinatorics enters into the picture. Some kind of analytic expression is needed for the distribution of is n (w) Such an expression is provided by the following result of Ira Gessel [14], later proved in other ways by various persons. Theorem. Let u k (n) #fw 2 S n : is n (w) kg 16 U k (x) u k (n) B i (x) 2n i n (n i) Then U k (x) det B ji jj (x) k i;j=1 Example. We have U 2 (x) B 0 (x) B 1 (x) From this it is easy to deduce ....
I. Gessel, Symmetric functions and P-recursiveness, J. Combinatorial Theory (A) 53 (1990), 257-285.
A Combinatorial Approach to Representations of Lie Groups and.. - Mihailovs (1998) (Correct)
....us to compute various combinatorial and representation theoretical constants, in particular, the number of plane symplectic wave graphs with given number of vertices. Certainly, almost all the formulas and examples here belong to a folk lore and or can be found in many works, in particular, in [1, 5, 6, 15, 16, 17, 18, 19, 32, 34, 56, 57]. I am planning to give a more detailed review of the known results as well as literature in the continuation of my work [47] If it is not specified, a graph here means the graph in the most general sense, i.e. it can contain multiple edges, loops and some edges can be directed. The only ....
I. M. Gessel, Symmetric functions and P -recursiveness, J. Comb. Theory A, 53 (1990), 257-- 285.
Weighted Derangements And The Linearization Coefficients Of.. - Zeng (Correct)
.... the up down permutations of odd length on [n] Especially, if m = 2, we obtain the quasi orthogonality : p n1 (x)p n2 (x) ae n 1 n 2 ; if jn 1 Gamma n 2 j = 1; 0; otherwise: These results may be of some interest in the theory of coefficients extraction of symmetric functions (cf. [23]) Acknowledgements This work was done while the author was visiting Institute for Advanced Study as a member in 1989 1990 and supported by NSF Grant DMS 8610730. The author is also indebted to Professor Jet Wimp for helpful discussions and correspondence regarding Meixner Pollaczek polynomials, ....
IRA M. GESSEL, Symmetric functions and P-recursiveness, J. Combin. Theory Ser. A 53 (1990), 257-285.
Random Walks in Weyl Chambers and the Decomposition of Tensor .. - Grabiner, Magyar (1997) (2 citations) (Correct)
....homogenous differential equation with polynomial coefficients) or, equivalently, the coefficients are P recursive [13] satisfying a relation r p i (k)a k i = 0 for some polynomials p i . The Bessel function determinants of this section must clearly be related to the formulas of Gessel [4]. 5.1 The determinant technique All cases use the same basic technique for converting the formulas in (2) and (3) into a determinant, with the determinant coming from the sum over the symmetric group S n ,which is either the whole Weyl group or a subgroup of it. 12 The basic example is the ....
I. M. Gessel, "Symmetric Functions and P-recursiveness," J. Combin. Th. A 53(1990), 257--285.
A Symmetric Functions Approach To Stockhausen's Problem - Yen (1995) (Correct)
....on n symbols is an enumerative question that can be approached using the theory of symmetric functions for coefficient extraction in the generating series approach. A generalization of the problem leads to a combinatorial construction for the Stockhausen sequences. Although only known techniques [G] are used, these are sophisticated, and the problem serves as a useful study of these techniques, and the algebraic analysis gives partial information about the formulation of a bijective proof. The paper is organized as follows. In Section 2, we define a few classical symmetric functions, and ....
I. Gessel, Symmetric functions and P-recursiveness, J. Combinatorial Theory 53 (1990), 257--285.
Counting Paths In Young's Lattice - Gessel (1993) (5 citations) Self-citation (Gessel) (Correct)
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I. M. Gessel (1990), Symmetric functions and P-recursiveness, J. Combin. Theory Ser. A 53, 257-- 285.
Moments of Characteristic Polynomials Enumerate Two-Rowed.. - Strahov (2003) (Correct)
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Gessel I., Symmetric functions and P-recursiveness. 1990 J. Combin. Theory Ser. A 53 257--285.
On Non P-Recursiveness of Numbers of Matchings (Linear Chord.. - Klazar (Correct)
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Gessel, I. M., "Symmetric functions and P-recursiveness." J. Comb. Theory, Ser. A 53(1990), 257--285.
Counting 1324-avoiding Permutations - Marinov, Radoicic (2003) (1 citation) (Correct)
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Ira M. Gessel, Symmetric functions and P-recursiveness, J. Combin. Theory Ser. A 53 (1990), no. 2, 257-285.
Four Classes of Pattern-Avoiding Permutations under one Roof: .. - Bousquet-Melou (2003) (Correct)
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I. M. Gessel. Symmetric functions and P-recursiveness. J. Combin. Theory Ser. A, 53(2):257--285, 1990.
The Füredi-Hajnal Conjecture Implies the Stanley-Wilf Conjecture - Klazar (Correct)
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I.M. Gessel, Symmetric functions and P-recursiveness, J. Comb. Theory, Ser. A 53 (1990), 257--285.
Four Classes of Pattern-Avoiding Permutations under one Roof: .. - Bousquet-Melou (2003) (Correct)
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I. M. Gessel. Symmetric functions and P-recursiveness. J. Combin. Theory Ser. A, 53(2):257-285, 1990.
Orthogonal Polynomial Ensembles in Probability Theory - König (2004) (Correct)
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I.M. Gessel, Symmetric functions and p-recursiveness, J. Comb. Theory A, 53, 257--285 (1990).
231-Avoiding Involutions and Fibonacci Numbers - Egge, Mansour (2002) (Correct)
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I. M. Gessel. Symmetric functions and P-recursiveness. J. Combin. Theory, Series A, 53:257--285, 1990.
Permutations Avoiding Two Patterns of Length Three - Vatter (2003) (Correct)
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I. Gessel, Symmetric functions and P-recursiveness, J. Combin. Theory Ser. A 53 (1990), 257-285.
Prefix Exchanging and Pattern Avoidance by Involutions - Jaggard (2003) (Correct)
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Ira M. Gessel, Symmetric functions and P-recursiveness, J. Combin. Theory Ser. A 53 (1990), no. 2, 257--285.
Prefix Exchanging And Pattern Avoidance By Involutions - Jaggard (2003) (Correct)
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Ira M. Gessel, Symmetric functions and P-recursiveness, J. Combin. Theory Ser. A 53 (1990), no. 2, 257-285.
Füredi-Hajnal Conjecture Implies Stanley-Wilf Conjecture - Klazar (1999) (Correct)
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I.M. Gessel, Symmetric functions and P-recursiveness, J. Combinatorial Th. Series A 53 (1990), 257--285.
Moments of Characteristic Polynomials Enumerate Two-Rowed.. - Strahov (2003) (Correct)
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Gessel I., Symmetric functions and P-recursiveness. 1990 J. Combin. Theory Ser. A 53 257-285.
Counting pattern-free set partitions I: A generalization of.. - Klazar (2000) (Correct)
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I.M. Gessel, Symmetric functions and P-recursiveness, J. Combinatorial Th. Series A 53 (1990), 257--285.
Permutations Avoiding Two Patterns of Length Three - Department (Correct)
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I. Gessel, Symmetric functions and P-recursiveness, J. Combin. Theory Ser. A 53 (1990), 257-285.
Counting 1324-avoiding Permutations - Marinov, Radoicic (2003) (1 citation) (Correct)
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Ira M. Gessel, Symmetric functions and P-recursiveness, J. Combin. Theory Ser. A 53 (1990), no. 2, 257--285.
Optimal Tail Estimates for Directed Last Passage.. - Baik, Deift.. (2001) (1 citation) (Correct)
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I. Gessel. Symmetric functions and P-recursiveness. J. Combin. Theory Ser. A, 53:257-285, 1990.
Counting Claw-Free Cubic Graphs - Edgar Palmer Ronald (Correct)
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I. M. Gessel, Symmetric functions and P-recursiveness, J. Combin. Theory Ser. A, 53 (1990), pp. 257-285.
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