Voir la notice de l'article provenant de la source Math-Net.Ru
@article{JSFU_2018_11_6_a15, author = {Georgy P. Egorychev}, title = {Permanents as formulas of summation over an algebra with a unique $n$-ary operation}, journal = {\v{Z}urnal Sibirskogo federalʹnogo universiteta. Matematika i fizika}, pages = {796--799}, publisher = {mathdoc}, volume = {11}, number = {6}, year = {2018}, language = {en}, url = {http://geodesic.mathdoc.fr/item/JSFU_2018_11_6_a15/} }
TY - JOUR AU - Georgy P. Egorychev TI - Permanents as formulas of summation over an algebra with a unique $n$-ary operation JO - Žurnal Sibirskogo federalʹnogo universiteta. Matematika i fizika PY - 2018 SP - 796 EP - 799 VL - 11 IS - 6 PB - mathdoc UR - http://geodesic.mathdoc.fr/item/JSFU_2018_11_6_a15/ LA - en ID - JSFU_2018_11_6_a15 ER -
%0 Journal Article %A Georgy P. Egorychev %T Permanents as formulas of summation over an algebra with a unique $n$-ary operation %J Žurnal Sibirskogo federalʹnogo universiteta. Matematika i fizika %D 2018 %P 796-799 %V 11 %N 6 %I mathdoc %U http://geodesic.mathdoc.fr/item/JSFU_2018_11_6_a15/ %G en %F JSFU_2018_11_6_a15
Georgy P. Egorychev. Permanents as formulas of summation over an algebra with a unique $n$-ary operation. Žurnal Sibirskogo federalʹnogo universiteta. Matematika i fizika, Tome 11 (2018) no. 6, pp. 796-799. http://geodesic.mathdoc.fr/item/JSFU_2018_11_6_a15/
[1] A. Barvinok, New permanent estimators via noncommutative determinants, 2000, 13 pp., arXiv: math/0007153
[2] I.M. Gelfand, V.S. Retakh, “Determinants of matrices over noncommutative rings”, Functional. Anal. and Prilozhen., 25:2 (1991), 91–102 | DOI | MR | Zbl
[3] G.P. Egorychev, “New formulas for the permanent”, Soviet Math. Dokl., 254:4 (1980), 784–787 | MR | Zbl
[4] G.P. Egorychev, “A new family of polynomial identities for computing determinants”, Math. Dokl., 2:1 (2013), 1–3 | MR
[5] V.V. Kochergin, “About complexity of computation one-terms of powers”, Discrete Analysis, 27, IM SO RAN, Novosibirsk, 1994, 94–107 (in Russian) | MR | Zbl
[6] Yu.D. Burago, V.A. Zalgaller, Geometric Inequalities, Springer Verlag, N.Y., 1988 | MR | Zbl
[7] G.P. Egorychev, Discrete mathematics. Permanents, Siberian Federal Univ., Krasnoyarsk, 2007 (in Russian) | MR
[8] H. Cartan, Elementary theory of analytic functions of one or several complex variables, Dover Publ., N.Y., 1995 | MR
[9] V.T. Filippov, “On the n-Lie algebra of Jacobians”, Sibirsk. Math. Zh., 39:3 (1998), 660–669 (in Russian) | MR | Zbl
[10] L.V. Sabinin, Methods of Nonassociative Algebra in Differential Geometry (in Supplement to Russian translation of S.K. Kobayashi and K. Nomizu "Foundations of Differential Geometry"), Nauka, M., 1981 (in Russian) | MR
[11] L. Chakhmakhchyan, N.J. Cerf, R. Garcia-Paton, Quantum-inspired algorithm for estimating the permanent of positive semidefinite matrices, 2017, 9 pp., arXiv: 1609.02416