Ribbon Matrices | המחלקה למתמטיקה

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. zoom אוניברסיטת בר-אילן - המחלקה למתמטיקה mathoffice@math.biu.ac.il Asia/Jerusalem public

Place

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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.