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Abstract: Young's lattice is the lattice of partitions of integers, ordered by inclusion of diagrams. Standard Young tableaux can be represented as paths in Young's lattice that go up by one square at each step, and more general paths in Young's lattice correspond to more general kinds of tableaux. Using the theory of symmetric functions, in particular Pieri's rule for multiplying a Schur function by a complete symmetric function, we derive formulas for counting paths in Young's lattice that go up or... (Update)
Context of citations to this paper: More
...supertableaux. In Section 6, we discuss commutation relations for the operators which add or delete horizontal or vertical strips (cf. [5, 6]) and give a generalization of these relations. In Section 7, we introduce a piecewise linear analogue of RSK for oscillating tableaux in...
...the following theorem. Theorem 4. The generating function P w( over all oscillating semistandard tableaux = i) fi ff (cf. [30, 11, 26]) with at most r rows equals (1.5) The weight w( is defined by Q x j (2i Gamma1) Gamma (2i) j j (2i Gamma1) Gamma (2i...
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BibTeX entry: (Update)
I. Gessel, Counting paths in Young's lattice, J. Stat. Plan. 34 (1993), 125--134. http://citeseer.ist.psu.edu/gessel93counting.html More
@article{ gessel93counting,
author = "I. Gessel",
title = "Counting paths in Young's lattice",
journal = "J. Stat. Plan.",
volume = "34";
pages = "125--134",
year = "1993",
url = "citeseer.ist.psu.edu/gessel93counting.html" }
Citations (may not include all citations):492 Symmetric Functions and Hall Polynomials (context) - Macdonald - 1979
47 Symmetric functions and P-recursiveness (context) - Gessel - 1990
46 American Mathematical Society (context) - Remmel, of et al. - 1984
27 and generalized Young tableaux (context) - Knuth, matrices - 1970
22 Robinson-Schensted algorithms for skew tableaux (context) - Sagan, Stanley - 1990
16 Applications and Extensions of Fomin's Generalization of the.. (context) - Roby
9 Schur operators and Knuth correspondences - Fomin - 1992
6 the Combinatorics of Representations of Sp (context) - Sundaram - 1986
5 The Cauchy identity for Sp (context) - Sundaram - 1990
5 function series (context) - Lascoux, Pragacz - 1988
4 An analogue to Robinson-Schensted correspondence for oscilla.. (context) - Delest, Dulucq et al. - 1988
1 Variations on di#erential posets (context) - Stanley - 1990
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