Return polynomials for non-intersecting paths above a surface on the directed square lattice

Journal of Physics A: Mathematical and General

Volumn 34, Issue 49, 2001, Pages 10763-10782

  Brak, R ^a   Essam, J W ^b  

^a UNIVERSITY OF MELBOURNE   (Australia)

^b UNIVERSITY OF LONDON   (United Kingdom)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0035862006     PISSN: 03054470     EISSN: None     Source Type: Journal    
DOI: 10.1088/0305-4470/34/49/303     Document Type: Article

References (20)

1. Fisher M E 1984 J. Stat. Phys. 34 667
2. Stanley R P 1997 Enumerative Combinatorics vol 1 (Cambridge: Cambridge University Press)
3. Stanton D and White D 1986 Constructive Combinatorics (New York: Springer)
4. Brak R, Essam J and Owczarek A L 2001 Scaling analysis for the absorption transition in a watermelon network of n directed non-intersecting walks J. Stat. Phys. 102 997
5. Brak R, Essam J W and Owczarek A 1998 New results for directed vesicles and chains near an attractive wall J. Stat. Phys. 93 155
6. Forrester P J 1989 J. Phys. A: Math. Gen. 22 L609
7. Arrowsmith D K, Mason P and Essam J W 1991 Physica A 177 267
8. Essam J W and Guttmann A J 1995 Phys. Rev. E 52 5849
9. Gessel I M and Viennot X 1989 Determinants, paths, and plane partitions Preprint
10. Gessel I M and Viennot X 1985 Adv. Math. 58 300
11. Guttmann A J, Owczarek A L and Viennot X G 1998 J. Phys. A: Math. Gen. 31 8123
12. Zeilberger D J 1991 Symb. Comput. 11 195
13. Krattenthaler C, Guttmann A J and Viennot X G 1999 J. Phys. A: Math. Gen. 33 8835
14. Proctor R A 1983 Proc. Am. Math. Soc. 89 553
15. Brak R, Essam J and Owczarek A L 1999 Exact solution of n directed non-intersecting walks interacting with one or two boundaries J. Phys. A: Math. Gen. 32 2921
16. Brak R, Essam J and Owczarek A L 1999 Partial difference equation method for lattice path problems Ann. Comb. 3 265
17. Brak R, Essam J and Owczarek A L 1998 From the Bethe ansatz to the Gessel-Viennot theorem Ann. Comb. 3 251
18. Riordan J 1968 Combinatorial Identities (New York: Wiley)
19. Dodgson C L 1866 Proc. R. Soc. 15 150
20. Krattenthaler C 1999 Advanced determinant calculus Seminaire Lotharingien Combinatoroire ('The Andrews Festschrift') 42 67