The many faces of alternating-sign matrices

by: J Propp

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Equivalence with square ice, gasket/basket, loop packing models

yaroslavvb (public ) - 2007-12-18 05:01:59

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Abstract

Introduction An alternating-sign matrix of order n is an n-by-n array of 0's, +1's and 1's with the property that in each row and each column, the non-zero entries alternate in sign, beginning and ending with a +1. For example, Figure 1 shows an alternating-sign matrix (ASM for short) of order 4. 0 B B @ 0 +1 0 0 +1 1 +1 0 0 0 0 +1 0 +1 0 0 1 C C A Figure 1: An alternating-sign matrix of order 4. Figure 2 exhibits all seven of the ASMs of order 3. 0 @ 0 0 +1 0 +1 0 +1 0 0 1 A 0 @ 0...

@misc{citeulike:2139481, abstract = {Introduction An alternating-sign matrix of order n is an n-by-n array of 0's, +1's and 1's with the property that in each row and each column, the non-zero entries alternate in sign, beginning and ending with a +1. For example, Figure 1 shows an alternating-sign matrix (ASM for short) of order 4. 0 B B @ 0 +1 0 0 +1 1 +1 0 0 0 0 +1 0 +1 0 0 1 C C A Figure 1: An alternating-sign matrix of order 4. Figure 2 exhibits all seven of the ASMs of order 3. 0 @ 0 0 +1 0 +1 0 +1 0 0 1 A 0 @ 0...}, author = {Propp, J. }, citeulike-article-id = {2139481}, comment = {* Equivalence with square ice, gasket/basket, loop packing models}, keywords = {combinatorics}, posted-at = {2007-12-18 05:01:59}, priority = {2}, title = {The many faces of alternating-sign matrices}, url = {http://citeseer.ist.psu.edu/447933.html} }

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TY - GEN ID - citeulike:2139481 L3 - citeulike-article-id:2139481 TI - The many faces of alternating-sign matrices N2 - Introduction An alternating-sign matrix of order n is an n-by-n array of 0's, +1's and 1's with the property that in each row and each column, the non-zero entries alternate in sign, beginning and ending with a +1. For example, Figure 1 shows an alternating-sign matrix (ASM for short) of order 4. 0 B B @ 0 +1 0 0 +1 1 +1 0 0 0 0 +1 0 +1 0 0 1 C C A Figure 1: An alternating-sign matrix of order 4. Figure 2 exhibits all seven of the ASMs of order 3. 0 @ 0 0 +1 0 +1 0 +1 0 0 1 A 0 @ 0... KW - combinatorics N1 - * Equivalence with square ice, gasket/basket, loop packing models AU - Propp, J UR - http://citeseer.ist.psu.edu/447933.html ER -

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