Differential posets and smith normal forms

Alexander Miller; Victor Reiner

doi:10.1007/s11083-009-9114-z

Differential posets and smith normal forms

Alexander Miller, Victor Reiner

School of Mathematics

Research output: Contribution to journal › Article › peer-review

14 Scopus citations

Abstract

We conjecture a strong property for the up and down maps U and D in an r-differential poset: DU + tI and UD + tI have Smith normal forms over z[t]. In particular, this would determine the integral structure of the maps U, D, UD, DU, including their ranks in any characteristic. As evidence, we prove the conjecture for the Young-Fibonacci lattice YF studied by Okada and its r-differential generalizations Z(r), as well as verifying many of its consequences for Young's lattice Y and the r-differential Cartesian products Y^r.

Original language	English (US)
Pages (from-to)	197-228
Number of pages	32
Journal	Order
Volume	26
Issue number	3
DOIs	https://doi.org/10.1007/s11083-009-9114-z
State	Published - Sep 2009

Keywords

Differential poset
Dual graded graphs
Invariant factors
Smith normal form

Publisher link

10.1007/s11083-009-9114-z

Find It

Find It at U of M Libraries

Cite this

@article{cfeb944bac1845d2a1715a636743fd42,

title = "Differential posets and smith normal forms",

abstract = "We conjecture a strong property for the up and down maps U and D in an r-differential poset: DU + tI and UD + tI have Smith normal forms over z[t]. In particular, this would determine the integral structure of the maps U, D, UD, DU, including their ranks in any characteristic. As evidence, we prove the conjecture for the Young-Fibonacci lattice YF studied by Okada and its r-differential generalizations Z(r), as well as verifying many of its consequences for Young's lattice Y and the r-differential Cartesian products Yr.",

keywords = "Differential poset, Dual graded graphs, Invariant factors, Smith normal form",

author = "Alexander Miller and Victor Reiner",

year = "2009",

month = sep,

doi = "10.1007/s11083-009-9114-z",

language = "English (US)",

volume = "26",

pages = "197--228",

journal = "Order",

issn = "0167-8094",

publisher = "Springer Netherlands",

number = "3",

}

TY - JOUR

T1 - Differential posets and smith normal forms

AU - Miller, Alexander

AU - Reiner, Victor

PY - 2009/9

Y1 - 2009/9

N2 - We conjecture a strong property for the up and down maps U and D in an r-differential poset: DU + tI and UD + tI have Smith normal forms over z[t]. In particular, this would determine the integral structure of the maps U, D, UD, DU, including their ranks in any characteristic. As evidence, we prove the conjecture for the Young-Fibonacci lattice YF studied by Okada and its r-differential generalizations Z(r), as well as verifying many of its consequences for Young's lattice Y and the r-differential Cartesian products Yr.

AB - We conjecture a strong property for the up and down maps U and D in an r-differential poset: DU + tI and UD + tI have Smith normal forms over z[t]. In particular, this would determine the integral structure of the maps U, D, UD, DU, including their ranks in any characteristic. As evidence, we prove the conjecture for the Young-Fibonacci lattice YF studied by Okada and its r-differential generalizations Z(r), as well as verifying many of its consequences for Young's lattice Y and the r-differential Cartesian products Yr.

KW - Differential poset

KW - Dual graded graphs

KW - Invariant factors

KW - Smith normal form

UR - http://www.scopus.com/inward/record.url?scp=70349257209&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=70349257209&partnerID=8YFLogxK

U2 - 10.1007/s11083-009-9114-z

DO - 10.1007/s11083-009-9114-z

M3 - Article

AN - SCOPUS:70349257209

SN - 0167-8094

VL - 26

SP - 197

EP - 228

JO - Order

JF - Order

IS - 3

ER -

Differential posets and smith normal forms

Abstract

Keywords

Publisher link

Find It

Other files and links

Fingerprint

Cite this