Proves symmetry for boundary-defect off-diagonally symmetric tilings of odd Aztec diamonds and gives Pfaffian formulas for nearly symmetric cases via non-intersecting paths and Delannoy numbers.
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The number of off-diagonally symmetric domino tilings of the Aztec diamond equals a Pfaffian of a matrix whose entries obey a simple recurrence.
Gives an unsigned determinant formula for the total weight of non-intersecting path families in upward-planar DAGs, with matrix entries being signed path counts.
citing papers explorer
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Off-diagonally symmetric domino tilings of the Aztec diamond of odd order
Proves symmetry for boundary-defect off-diagonally symmetric tilings of odd Aztec diamonds and gives Pfaffian formulas for nearly symmetric cases via non-intersecting paths and Delannoy numbers.
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Off-diagonally symmetric domino tilings of the Aztec diamond
The number of off-diagonally symmetric domino tilings of the Aztec diamond equals a Pfaffian of a matrix whose entries obey a simple recurrence.
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An extension of the Lindstr\"om-Gessel-Viennot theorem
Gives an unsigned determinant formula for the total weight of non-intersecting path families in upward-planar DAGs, with matrix entries being signed path counts.