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  • 1.
    Sjöstrand, Jonas
    KTH.
    Cylindrical lattice walks and the Loehr-Warrington 10(n) conjecture2007In: European journal of combinatorics (Print), ISSN 0195-6698, E-ISSN 1095-9971, Vol. 28, no 3, p. 774-780Article in journal (Refereed)
    Abstract [en]

    The following special case of a conjecture by Loehr and Warrington was proved recently by Ekhad, Vatter. and Zeilberger:

    There are 10(n) zero-sum words of length 5n in the alphabet {+3, -2} such that no zero-sum consecutive subword that starts with +3 may be followed immediately by -2.

    We give a simple bijective proof of the conjecture in its original and more general setting. To do this we reformulate the problem in terms of cylindrical lattice walks. (c) 2005 Elsevier Ltd. All rights reserved.

  • 2.
    Sjöstrand, Jonas
    Royal Institute of Technology, Sweden.
    On the sign-imbalance of skew partition shapes2007In: European journal of combinatorics (Print), ISSN 0195-6698, E-ISSN 1095-9971, Vol. 28, no 6, p. 1582-1594Article in journal (Refereed)
    Abstract [en]

    Let the sign of a skew standard Young tableau be the sign of the permutation you get by reading it row by row from left to right, like a book. We examine how the sign property is transferred by the skew Robinson-Schensted correspondence invented by Sagan and Stanley. The result is a remarkably simple generalization of the ordinary non-skew formula. The sum of the signs of all standard tableaux on a given skew shape is the sign-imbalance of that shape. We generalize previous results on the sign-imbalance of ordinary partition shapes to skew ones. 

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