کد مقاله کد نشریه سال انتشار مقاله انگلیسی نسخه تمام متن
6419729 1631647 2011 27 صفحه PDF دانلود رایگان
عنوان انگلیسی مقاله ISI
A unifying poset perspective on alternating sign matrices, plane partitions, Catalan objects, tournaments, and tableaux
موضوعات مرتبط
مهندسی و علوم پایه ریاضیات ریاضیات کاربردی
پیش نمایش صفحه اول مقاله
A unifying poset perspective on alternating sign matrices, plane partitions, Catalan objects, tournaments, and tableaux
چکیده انگلیسی

Alternating sign matrices (ASMs) are square matrices with entries 0, 1, or −1 whose rows and columns sum to 1 and whose nonzero entries alternate in sign. We present a unifying perspective on ASMs and other combinatorial objects by studying a certain tetrahedral poset and its subposets. We prove the order ideals of these subposets are in bijection with a variety of interesting combinatorial objects, including ASMs, totally symmetric self-complementary plane partitions (TSSCPPs), staircase shaped semistandard Young tableaux, Catalan objects, tournaments, and totally symmetric plane partitions. We prove product formulas counting these order ideals and give the rank generating function of some of the corresponding lattices of order ideals. We also prove an expansion of the tournament generating function as a sum over TSSCPPs. This result is analogous to a result of Robbins and Rumsey expanding the tournament generating function as a sum over alternating sign matrices.

ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Advances in Applied Mathematics - Volume 46, Issues 1–4, January 2011, Pages 583-609
نویسندگان
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