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Transactions of the American Mathematical Society

Published by the American Mathematical Society, the Transactions of the American Mathematical Society (TRAN) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6850 (online) ISSN 0002-9947 (print)

The 2020 MCQ for Transactions of the American Mathematical Society is 1.43.

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A remarkable formula for counting nonintersecting lattice paths in a ladder with respect to turns
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by C. Krattenthaler and M. Prohaska PDF
Trans. Amer. Math. Soc. 351 (1999), 1015-1042 Request permission

Abstract:

We prove a formula, conjectured by Conca and Herzog, for the number of all families of nonintersecting lattice paths with certain starting and end points in a region that is bounded by an upper ladder. Thus we are able to compute explicitly the Hilbert series for certain one-sided ladder determinantal rings.
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Additional Information
  • C. Krattenthaler
  • Affiliation: Institut für Mathematik der Universität Wien, Strudlhofgasse 4, A-1090 Wien, Austria
  • MR Author ID: 106265
  • Email: kratt@pap.univie.ac.at
  • M. Prohaska
  • Affiliation: Institut für Mathematik der Universität Wien, Strudlhofgasse 4, A-1090 Wien, Austria
  • Received by editor(s): January 11, 1996
  • Additional Notes: The first author was supported in part by EC’s Human Capital and Mobility Program grant CHRX-CT93-0400 and the Austrian Science Foundation FWF, grant P10191-MAT
  • © Copyright 1999 American Mathematical Society
  • Journal: Trans. Amer. Math. Soc. 351 (1999), 1015-1042
  • MSC (1991): Primary 05A15, 13C40; Secondary 05A19, 13F50, 13H10
  • DOI: https://doi.org/10.1090/S0002-9947-99-01884-X
  • MathSciNet review: 1407495