Pólya convertibility problem for symmetric matrices

A. Guterman; G. Dolinar; B. Kuz'ma

doi:10.1134/s0001434612110053

Pólya convertibility problem for symmetric matrices

A. Guterman, G. Dolinar, B. Kuz'ma

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

Abstract

We investigate symmetric (0, 1) matrices on which the permanent is convertible to the determinant by assigning ± signs to their entries. In particular, we obtain several quantitative bounds for the number of nonzero elements of such matrices, including the analog of Gibson's theorem for symmetric matrices.

Original language	English
Pages (from-to)	624-635
Number of pages	12
Journal	Mathematical Notes
Volume	92
Issue number	5-6
DOIs	https://doi.org/10.1134/s0001434612110053
State	Published - 2012
Externally published	Yes

Keywords

conversion
determinant
permanent
symmetric matrix

All Science Journal Classification (ASJC) codes

General Mathematics

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10.1134/s0001434612110053

Cite this

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title = "P{\'o}lya convertibility problem for symmetric matrices",

abstract = "We investigate symmetric (0, 1) matrices on which the permanent is convertible to the determinant by assigning ± signs to their entries. In particular, we obtain several quantitative bounds for the number of nonzero elements of such matrices, including the analog of Gibson's theorem for symmetric matrices.",

keywords = "conversion, determinant, permanent, symmetric matrix",

author = "A. Guterman and G. Dolinar and B. Kuz'ma",

note = "Funding Information: The work is supported in part by the joint Slovenian–Russian grant no. BI-RU/12-13-022. The work of the first author is also partially supported by grant no. MD-2502.2012.1 and by the Russian Foundation for Basic Research (grant no. 12-01-00140-a).",

year = "2012",

doi = "10.1134/s0001434612110053",

language = "الإنجليزيّة",

volume = "92",

pages = "624--635",

journal = "Mathematical Notes",

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AU - Dolinar, G.

AU - Kuz'ma, B.

N1 - Funding Information: The work is supported in part by the joint Slovenian–Russian grant no. BI-RU/12-13-022. The work of the first author is also partially supported by grant no. MD-2502.2012.1 and by the Russian Foundation for Basic Research (grant no. 12-01-00140-a).

PY - 2012

Y1 - 2012

N2 - We investigate symmetric (0, 1) matrices on which the permanent is convertible to the determinant by assigning ± signs to their entries. In particular, we obtain several quantitative bounds for the number of nonzero elements of such matrices, including the analog of Gibson's theorem for symmetric matrices.

AB - We investigate symmetric (0, 1) matrices on which the permanent is convertible to the determinant by assigning ± signs to their entries. In particular, we obtain several quantitative bounds for the number of nonzero elements of such matrices, including the analog of Gibson's theorem for symmetric matrices.

KW - conversion

KW - determinant

KW - permanent

KW - symmetric matrix

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U2 - 10.1134/s0001434612110053

DO - 10.1134/s0001434612110053

M3 - مقالة

SN - 0001-4346

VL - 92

SP - 624

EP - 635

JO - Mathematical Notes

JF - Mathematical Notes

IS - 5-6

ER -

Pólya convertibility problem for symmetric matrices

Abstract

Keywords

All Science Journal Classification (ASJC) codes

Access to Document

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