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Encyclopedia of Combinatorial Polytope Sequences


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Alternating Sign Matrix Polytope

(No 3d term.)
[ polymake for n=3]
• Alternating Sign Matrix polytopes ASM(n) [arXiv] (J. Striker)
• convex_hull({char_vector_ASM | ASM an nxn alternating sign matrix })
• Dimensions:
0, 1, 4, 9, 16, ... (n-1)^2
• Number of Vertices in nth polytope:
1, 2, 7, 42, 429, 7436,... Product[j=0..n-1](3j+1)!/(n+j)! [ OEIS A005130]
• Number of Facets:
0, 2, 4, 8, 20, 40, 68, 104,...,4[(n-2)^2 +1][ OEIS A128445]
• f-vectors:
1, 2, 1, 7, 17, 18, 8, 1, 42, ... [ OEIS ?]
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