**Demo mode:
there is a limit of max. 3 allowed answers for unregistered
users**

**
Subscription and pricing information**

**Your query: **an = (864.05087)### Answers 1-1 (of 1)

[New query form]

864.05087

**Ghorpade, Sudhir R.**

**Young multitableaux and higher dimensional determinants.** (English)

[J] Adv. Math. 121, No.2, 167-195, Art. No.0051 (1996). [ISSN 0001-8708]

A standard Young multitableau of width $q>0$ bounded by $m=(m(1),\dots,m(q))$ is a $q$-tuple of standard Young tableaux of the same shape such that the entries of the $i$th tableau are bounded by $m(i)$. Let $\text{stab}(q,m,p,a,V)$ be the number of the standard multitableaux $T$ of width $q$, with $V$ boxes, bounded by $m$ and predominated by the multivector $a$ of width $q$ and length $p$ (i.e. placing $a$ before the first row of $T$, the resulting tableau is standard again). The main result of the paper under review is a formula which, fixing $q$ even, $p$, $m$ and $a$, gives a polynomial in $V$ which is equal to the cardinality of $\text{stab}(q,m,p,a,V)$. The main motivation for this result comes from the work of Abhyankar on enumerating Young multitableaux. It also generalizes the important Abhyankar formula for $\text{stab}(2,m,p,a,V)$ which is a basic ingredient of Abhyankar's enumerative proof of the straightening law of Doubilet-Rota-Stein. Using the notion of a $q$-dimensional determinant, as a consequence of the main result of this paper, the author shows that the natural generalization of the straightening law for multitableaux is not true in general for even $q>2$. The author also answers several problems posed in [{\it S. S. Abhyankar}, Enumerative combinatorics of Young tableaux, Dekker, New York-Basel (1988; Zbl 643.05001)].

[ **V.Drensky (Sofia)** ]
*MSC 1991: *-
*05E10 Tableaux, etc.

15A15 Special matrix functions

05A15 Combinatorial enumeration problems

05A10 Combinatorial functions

*Keywords: *Young multitableau; Young tableaux; Abhyankar formula; straightening law

*Citations: *Zbl 643.05001

*Cited in Zbl. reviews...*

Link to full text On line ordering services

[New query form]### Answers 1-1 (of 1)

**Zentralblatt MATH**,

*Copyright (c) 2000 European Mathematical Society, FIZ Karlsruhe & Springer-Verlag.*