Ribbon Matrices
Seminar
Speaker
Harel Rozenfeld (BIU)
Date
31/10/2021 - 15:30 - 14:00Add to Calendar
2021-10-31 14:00:00
2021-10-31 15:30:00
Ribbon Matrices
An r-ribbon tableau of shape λ⊢ rn is a filling of the cells of the diagram [λ] by the letters 1, . . . , n
such that each letter fills exactly r cells, which form a ribbon shape,
and for each 1 ≤ k ≤ n, the union of the i-th ribbons for 1 ≤ i ≤ k is a diagram of ordinary shape.
A ribbon matrix of order n is an n-ribbon tableau whose shape is an nxn square.
We present a new bijection from the set of ribbon matrices of order nxn to the set of permutations in the symmetric group S_n.
Using the bijection, we characterize the anti-diagonal of a ribbon matrix and show that the number of matrices in which
the numbers 1, . . . , n appear in the anti-diagonal in an ascending order is an interlacing Genocchi number.
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אוניברסיטת בר-אילן - Department of Mathematics
mathoffice@math.biu.ac.il
Asia/Jerusalem
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Abstract
An r-ribbon tableau of shape λ⊢ rn is a filling of the cells of the diagram [λ] by the letters 1, . . . , n
such that each letter fills exactly r cells, which form a ribbon shape,
and for each 1 ≤ k ≤ n, the union of the i-th ribbons for 1 ≤ i ≤ k is a diagram of ordinary shape.
A ribbon matrix of order n is an n-ribbon tableau whose shape is an nxn square.
We present a new bijection from the set of ribbon matrices of order nxn to the set of permutations in the symmetric group S_n.
Using the bijection, we characterize the anti-diagonal of a ribbon matrix and show that the number of matrices in which
the numbers 1, . . . , n appear in the anti-diagonal in an ascending order is an interlacing Genocchi number.
Last Updated Date : 01/11/2021
