A remarkable formula for counting nonintersecting lattice paths in a ladder with respect to turns

Authors
Krattenthaler, C Prohaska, M
Citation
C. Krattenthaler et M. Prohaska, A remarkable formula for counting nonintersecting lattice paths in a ladder with respect to turns, T AM MATH S, 351(3), 1999, pp. 1015-1042
Citations number
22
Categorie Soggetti
Mathematics
Journal title
TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY
ISSN journal
00029947 → ACNP
Volume
351
Issue
3
Year of publication
1999
Pages
1015 - 1042
Database
ISI
SICI code
0002-9947(199903)351:3<1015:ARFFCN>2.0.ZU;2-S
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 poi nts in a region that is bounded by an upper ladder. Thus we are able to com pute explicitly the Hilbert series for certain one-sided ladder determinant al rings.