A q,t-analogue of Narayana numbers

Jean-Christophe Aval; Michele D'Adderio; Mark Dukes; Angela Hicks; Yvan Le Borgne

A q,t-analogue of Narayana numbers

Jean-Christophe Aval, Michele D'Adderio, Mark Dukes, Angela Hicks, Yvan Le Borgne

Research output: Chapter in Book/Report/Conference proceeding › Chapter

Abstract

We study the statistics area, bounce and dinv associated to polyominoes in a rectangular box m times n. We show that the bi-statistics (area, bounce) and (area, dinv) give rise to the same q, t-analogue of Narayana numbers, which was introduced by two of these authors in a recent paper. We prove the main conjectures of that same work, i.e. the symmetries in q and t, and in m and n of these polynomials, by providing a symmetric functions interpretation which relates them to the famous diagonal harmonics.

Original language	English
Title of host publication	DMTCS Proceedings
Subtitle of host publication	25th International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2013)
Place of Publication	Nancy, France
Pages	623-634
Number of pages	12
Publication status	Published - 2013

Keywords

q, t-Narayana
rectangular polyominoes
parking functions

Cite this

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title = "A q,t-analogue of Narayana numbers",

abstract = "We study the statistics area, bounce and dinv associated to polyominoes in a rectangular box m times n. We show that the bi-statistics (area, bounce) and (area, dinv) give rise to the same q, t-analogue of Narayana numbers, which was introduced by two of these authors in a recent paper. We prove the main conjectures of that same work, i.e. the symmetries in q and t, and in m and n of these polynomials, by providing a symmetric functions interpretation which relates them to the famous diagonal harmonics.",

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author = "Jean-Christophe Aval and Michele D'Adderio and Mark Dukes and Angela Hicks and {Le Borgne}, Yvan",

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T1 - A q,t-analogue of Narayana numbers

AU - Aval, Jean-Christophe

AU - D'Adderio, Michele

AU - Dukes, Mark

AU - Hicks, Angela

AU - Le Borgne, Yvan

PY - 2013

Y1 - 2013

N2 - We study the statistics area, bounce and dinv associated to polyominoes in a rectangular box m times n. We show that the bi-statistics (area, bounce) and (area, dinv) give rise to the same q, t-analogue of Narayana numbers, which was introduced by two of these authors in a recent paper. We prove the main conjectures of that same work, i.e. the symmetries in q and t, and in m and n of these polynomials, by providing a symmetric functions interpretation which relates them to the famous diagonal harmonics.

AB - We study the statistics area, bounce and dinv associated to polyominoes in a rectangular box m times n. We show that the bi-statistics (area, bounce) and (area, dinv) give rise to the same q, t-analogue of Narayana numbers, which was introduced by two of these authors in a recent paper. We prove the main conjectures of that same work, i.e. the symmetries in q and t, and in m and n of these polynomials, by providing a symmetric functions interpretation which relates them to the famous diagonal harmonics.

KW - q, t-Narayana

KW - rectangular polyominoes

KW - parking functions

UR - http://www.dmtcs.org/dmtcs-ojs/index.php/dmtcs

UR - http://www.dmtcs.org/dmtcs-ojs/index.php/proceedings/article/view/dmAS0153/4236

M3 - Chapter

SP - 623

EP - 634

BT - DMTCS Proceedings

CY - Nancy, France

ER -

A q,t-analogue of Narayana numbers

Abstract

Keywords

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