Plane Partition Diamonds and Generalizations
نویسنده
چکیده
SYLVIE CORTEEL AND CARLA D. SAVAGE Abstra t. In this note we generalize the plane partition diamonds of Andrews, Paule, and Riese to plane partition polygons and plane tree diamonds and show how to ompute their generating fun tions. 1. Introdu tion In [1℄, Andrews, Paule, and Riese introdu e the family of plane partition diamonds. A plane partition diamond of length n is a sequen e of length 3n + 1 of nonnegative integers a = (a1; : : : ; a3n+1) satisfying, for 0 i n 1, a3i+1 a3i+2; a3i+1 a3i+3; a3i+2 a3i+4; a3i+3 a3i+4: This is shown graphi ally below. a4 a7 a3n+1 a2 a5 a3n−1 a1 a3 a6 a3n a3n−2 . . . The on guration (7; 5; 5; 5; 4; 5; 2; 1; 1; 0; 0; 0; 0) is a plane partition diamond of length 4 : 5
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