caa a22 4500 388092084 CHVBK 20180307125254.0 cr unu---uuuuu 161130e199906 xx s 000 0 eng 10.1017/S0004972700033062 doi S0004972700033062 pii (NATIONALLICENCE)cambridge-10.1017/S0004972700033062 Cho Soojin ChungGu NaRae Apt. 102-901, ChunMin-Dong, Yusong-Gu, Taejon 305-390, Korea e-mail: sjcho@math.kaist.ac.kr Polytopes of roots of type AN [Elektronische Daten] [Soojin Cho] Polytopes of roots of type An−1 are investigated, which we call Pn. The polytopes, , of positive roots and the origin have been considered in relation to other branches of mathematics [4]. We show that exactly n copies of forms a disjoint cover of Pn. Moreover, those n copies of can be obtained by letting the elements of a subgroup of the symmetric group Sn generated by an n-cycle act on . We also characterise the faces of Pn and some facets of , which we believe to be useful in some optimisation problems. As by-products, we obtain an interesting identity on the number of lattice paths and a triangulation of the product of two simplices. Copyright © Australian Mathematical Society 1999 Bulletin of the Australian Mathematical Society Cambridge University Press 59/3(1999-06), 391-402 0004-9727 59:3<391 1999 59 BAZ https://doi.org/10.1017/S0004972700033062 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1017/S0004972700033062 text/html Onlinezugriff via DOI NATIONALLICENCE 100 1- Cho Soojin ChungGu NaRae Apt. 102-901, ChunMin-Dong, Yusong-Gu, Taejon 305-390, Korea e-mail: sjcho@math.kaist.ac.kr NATIONALLICENCE 773 0- Bulletin of the Australian Mathematical Society Cambridge University Press 59/3(1999-06), 391-402 0004-9727 59:3<391 1999 59 BAZ CC0 http://creativecommons.org/publicdomain/zero/1.0 nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-cambridge