This article is cited in 2 papers

Plane Partitions and Their Pedestal Polynomials

O. V. Ogievetskii^abc, S. B. Shlosman<sup>ade

a</sup> Aix-Marseille Université, CNRS, CPT UMR 7332, 13288 Marseille, France
^b Kazan (Volga Region) Federal University
^c P. N. Lebedev Physical Institute of the Russian Academy of Sciences, Moscow
^d Institute for Information Transmission Problems of the Russian Academy of Sciences (Kharkevich Institute), Moscow
^e Skolkovo Institute of Science and Technology

Abstract: For a linear extension $P$ of a partially ordered set $\mathscr S$, we define a multivariate polynomial by counting certain reverse partitions on $\mathscr S$, called $P$-pedestals. We establish a remarkable property of this polynomial: it does not depend on the choice of $P$. For $\mathscr S$ a Young diagram, we show that this polynomial generalizes the hook polynomial.

Keywords: Young diagram, hook polynomial, Schur functions.

UDC: 512.6

Received: 06.02.2018

DOI: 10.4213/mzm11958

 English version: Mathematical Notes, 2018, 103:5, 793–796

Bibliographic databases:

• 
• 
• 
•