Paul Drube

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A tableau inversion is a pair of entries in row-standard tableau T that lie in the same column of T yet lack the appropriate relative ordering to make T columnstandard. An i-inverted Young tableau is a row-standard tableau along with precisely i inversion pairs. Tableau inversions were originally introduced by Fresse to calculate the Betti numbers of(More)
A tableau inversion is a pair of entries from the same column of a row-standard tableau that lack the relative ordering necessary to make the tableau columnstandard. An i-inverted Young tableau is a row-standard tableau with precisely i inversion pairs, and may be interpreted as a generalization of (column-standard) Young tableaux. Inverted Young tableaux(More)
It is well known that the number of distinct non-crossing matchings of n halfcircles in the half-plane with endpoints on the x-axis equals the nth Catalan number Cn. This paper generalizes that notion of linear non-crossing matchings, as well as the circular non-crossing matchings of Goldbach and Tijdeman, to non-crossings matchings of curves embedded(More)
The Raney numbers Rp,r(k) are a two-parameter generalization of the Catalan numbers that were introduced by Raney in his investigation of functional composition patterns. We give a new combinatorial interpretation for the Raney numbers in terms of planar embeddings of certain collections of trees, a construction that recovers the usual interpretation of the(More)
An inverted semistandard Young tableau is a row-standard tableau along with a collection of inversion pairs that quantify how far the tableau is from being column semistandard. Such a tableau with precisely k inversion pairs is said to be a k-inverted semistandard Young tableau. Building upon earlier work by Fresse and the author, this paper develops(More)
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