Oscillating tableaux and nonintersecting lattice paths

Journal of Statistical Planning and Inference

Volumn 54, Issue 1, 1996, Pages 75-85

  Krattenthaler, C ^a  

^a UNIVERSITY OF VIENNA   (Austria)

Author keywords

Nonintersecting lattice paths; Oscillating tableaux

Indexed keywords

EID: 0030565370     PISSN: 03783758     EISSN: None     Source Type: Journal    
DOI: 10.1016/0378-3758(96)00158-9     Document Type: Article

References (38)

1. Berele, A. (1986). A Schensted-type correspondence for the symplectic group. J. Combin. Theory Ser. A 43, 320-328.
2. Brenti, F. (1993). Determinants of super-Schur functions, lattice paths, and dotted plane partitions. Adv. Math. 98, 27-64.
3. Brenti, F. (1995). Combinatorics and total positivity. J. Combin. Theory Ser. A 71, 175-218.
4. Bressoud, D.M. and S.-Y. Wei (1992). Determinental formulae for complete symmetric functions. J. Combin. Theory Ser. A 60, 277-286.
5. Choi, S.H. and D. Gouyou-Beauchamps (1993). Enumération de tableaux de Young semi-standard. Theoret. Computer Science 117, 137-151.
6. Comtet L. (1974). Advanced Combinatorics (D. Reidel, Dordrecht).
7. Conca, A. (1994). Gröbner bases of ideals of minors of a symmetric matrix. J. Algebra 166, 406-421.
8. Conca, A. (1995). Ladder determinantal rings. J. Pure Appl Algebra 98, 119-134.
9. Conca, A. and J. Herzog (1994). On the Hilbert function of determinantal rings and their canonical module. Proc. Amer. Math. Soc. 122, 677-681.
10. Desainte-Catherine, M. and G. Viennot (1986). Enumeration of certain Young tableaux with bounded height, In: G. Labelle, P. Leroux, Eds. Combinatoire enumérative. Springer Berlin, 58-67.
11. Doran, W.F. (1993). A connection between alternating sign matrices and totally symmetric self-complementary plane partitions. J. Combin. Theory Ser. A 64, 265-288.
12. Fulmek, M. and C. Krattenthaler (1995). Lattice path proofs for determinant formulas for symplectic and orthogonal characters. J. Combin. Theory Ser. A (to appear).
13. Gessel, I.M. (1993). Counting paths in Young's lattice. J. Statist. Plann. Inference 34, 125-134.
14. Gessel, I.M. and C. Krattenthaler (1995). Cylindric partitions. Trans. Amer. Math. Soc. (to appear).
15. Gessel, I.M. and G. Viennot (1985). Binomial determinants, paths, and hook length formulae. Adv. Math. 58, 300-321.
16. Gessel, I.M. and G. Viennot (1989). Determinants, paths, and plane partitions. preprint.
17. Greene, C. (1992). Proof of a conjecture on immanents of the Jacobi-Trudi matrix. Linear Algebra Appl. 171, 65-79.
18. Herzog, J and N.V. Trung (1992). Gröbner bases and multiplicity of determinantal and Pfaffian ideals. Adv. Math. 96, 1-37.
19. Krattenthaler, C. (1993). Non-crossing two-rowed arrays and summations for Schur functions. In: A. Barlotti, M. Delest, R. Pinzani, Eds., Proc. 5th Conf. on Formal Power Series and Algebraic Combinatorics, Florence, D.S.I., Università di Firenze, 301-314.
20. Krattenthaler, C. (1996). Non-crossing two-rowed arrays (in preparation).
21. Krattenthaler, C. (1995). The major counting of nonintersecting lattice paths and generating functions for tableaux. Mem. Amer. Math. Soc. 115, no. 552, Providence, R.I.
22. Krattenthaler, C. and S.G. Mohanty (1995). Counting tableaux with row and column bounds. Discrete Math. 139, 273-286.
23. Kulkarni, D.M. (1993a). Counting of path-like objects and coefficients of Hilbert polynomial of a determinantal ideal. preprint.
24. Kulkarni, D.M. (1993b). Counting of paths and coefficients of Hilbert polynomial of a determinantal ideal. preprint.
25. Macdonald, I.G. (1979). Symmetric Functions and Hall Polynomials. Oxford University Press, New York/London.
26. Modak, M.R. (1992). Combinatorial meaning of the coefficients of a Hilbert polynomial. Proc. Indian Acad. Sci. (Math. Sci) 102, 93-123.
27. Okada, S. (1990) Partially strict shifted plane partitions. J. Combin. Theory Ser. A 53, 143-156.
28. Okada, S. (1991). Lattice path method and characters of classical groups. preprint.
29. Remmel, J.B. and R. Whitney (1983). A bijective proof of the hook formula for the number of column-strict tableaux with bounded entries, Eur. J. Combin. 4, 45-63.
30. Remmel, J.B. and R. Whitney (1984). A bijective proof of the generating function for the number of reverse plane partitions via lattice paths. Linear Multilinear Algebra 16, 75-91.
31. Roby, T.W. (1991). Applications and extensions of Fomin's generalization of the Robinson-Schensted correspondence to differential posets. Ph.D. Thesis, MIT, Cambridge, Ma.
32. Sagan, B.E. (1989). The ubiquitous Young tableau In: D. Stanton, ed. Invariant theory and tableaux. The IMA Volumes in Math. And Its Appl., Vol. 19, Springer, New York, 262-298.
33. Sagan, B.E. (1992). Log concave sequences of symmetric functions and analogs of the Jacobi-Trudi determinants. Trans. Amer. Math. Soc. 329, 795-811.
34. Stembridge, J.R. (1990). Nonintersecting paths, pfaffians and plane partitions. Adv. Math. 83, 96-131.
35. Stembridge, J.R. (1995). The enumeration of totally symmetric plane partitions. Adv. in Math. 111, 227-245.
36. Sulanke, R.A. (1990). A determinant for q-counting lattice paths. Discrete Math. 81, 91-96.
37. Sundaram, S. (1986). On the combinatorics of representations of Sp(2n, ℂ). Ph. D. Thesis, Massachusetts Institute of Technology.
38. Ueno, K. (1991). Lattice path proof of the ribbon determinant formula for Schur functions. Nagoya Math. J. 124, 55-59.