Application of Hadamard product to some combinatorial and probabilistic problems
Diskretnaya Matematika, Tome 28 (2016) no. 1, pp. 101-112.

Voir la notice de l'article provenant de la source Math-Net.Ru

An improvement of the algebraic method of computing the Hadamard product of rational functions is given. Some applications of the Hadamard product to combinatorial and probabilistic problems are considered.
Keywords: Hadamard product, generating functions, rational power series.
@article{DM_2016_28_1_a5,
     author = {E. A. Potekhina},
     title = {Application of {Hadamard} product to some combinatorial and probabilistic problems},
     journal = {Diskretnaya Matematika},
     pages = {101--112},
     publisher = {mathdoc},
     volume = {28},
     number = {1},
     year = {2016},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/DM_2016_28_1_a5/}
}
TY  - JOUR
AU  - E. A. Potekhina
TI  - Application of Hadamard product to some combinatorial and probabilistic problems
JO  - Diskretnaya Matematika
PY  - 2016
SP  - 101
EP  - 112
VL  - 28
IS  - 1
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/DM_2016_28_1_a5/
LA  - ru
ID  - DM_2016_28_1_a5
ER  - 
%0 Journal Article
%A E. A. Potekhina
%T Application of Hadamard product to some combinatorial and probabilistic problems
%J Diskretnaya Matematika
%D 2016
%P 101-112
%V 28
%N 1
%I mathdoc
%U http://geodesic.mathdoc.fr/item/DM_2016_28_1_a5/
%G ru
%F DM_2016_28_1_a5
E. A. Potekhina. Application of Hadamard product to some combinatorial and probabilistic problems. Diskretnaya Matematika, Tome 28 (2016) no. 1, pp. 101-112. http://geodesic.mathdoc.fr/item/DM_2016_28_1_a5/

[1] Aizenberg L.A., Leinartas E.K., “Mnogomernaya kompozitsiya Adamara i yadra Sege”, Sibirskii matematicheskii zhurnal, 24:3 (1983), 3–10 | MR

[2] Elin M.M., “Mnogomernaya kompozitsiya Adamara”, Sibirskii matematicheskii zhurnal, 35:35 (1994), 1052–1057 | MR | Zbl

[3] Leinartas E.K., “Ob odnom obobschenii proizvedeniya Adamara v $C^{n}$”, Matematicheskie zametki, 32:4 (1982), 477–482 | MR

[4] De Loera J.A., Haws D., Hemmecke R., Yoshida R., “A computational study of integer programming algorithms based on Barvinok's rational functions”, Discrete Optimization, 2:2 (2005), 135–144 | DOI | MR | Zbl

[5] Bostan A., Boukraa S., Christol G., Hassani S., Maillard J-M., “Using $n$-fold integrals as diagonals of rational functions and integrality of series expansions”, J. Physics A: Math. and Theor., 46:18 (2013), 185201 | DOI | MR

[6] Zhilinskii B., “Generating functions for effective Hamiltonians via the symmetrized Hadamard product”, J. Physics A: Math. and Theor., 41:38 (2008), 382004 | DOI | MR | Zbl

[7] Stanley R., Enumerative Combinatorics, Wadsworth Brooks/Cole, 1984; Stenli R., Perechislitelnaya kombinatorika, Mir, Moskva, 1990, 440 pp. | MR

[8] Lando S.K., Lektsii o proizvodyaschikh funktsiyakh, MTsNMO, Moskva, 2007, 144 pp.

[9] Krivokolesko V.P., Leinartas E.K., “O tozhdestvakh s polinomialnymi koeffitsientami”, Izv. Irkutskogo gos. un-ta. Ser. Matem., 5:3 (2012), 56–62 | Zbl

[10] Rybnikov K.A., Kombinatornyi analiz. Ocherki istorii, Izd-vo mekh.-matem. f-ta MGU, Moskva, 1996, 125 pp.

[11] Han G.-N., “A general algorithm for the MacMahon omega operator”, Ann. Combinatorics, 7:4 (2003), 467–480 | DOI | MR | Zbl

[12] Potekhina E.A., Tolovikov M.I., “Raspredelenie serii v posledovatelnostyakh 1-zavisimykh indikatorov”, Cherepovetskie nauchnye chteniya - 2010: Mater. Vseros. nauch.-prakt. konf. Ch. 3: Tekhn., estestv. i ekon. nauki, 2011, 136–139, ChGU, Cherepovets

[13] Potekhina E.A., Tolovikov M.I., “Ostsilliruyuschee sluchainoe bluzhdanie i proizvedenie Adamara ratsionalnykh funktsii”, Diskretnaya matematika, 25:3 (2013), 96–115 ; Potekhina E. A., Tolovikov M. I., “Oscillating random walk and the Hadamard product of rational functions”, Discrete Math. Appl., 24:1 (2014), 29–44 | DOI | MR | DOI | Zbl

[14] Kim J.H., Hadamard products, lattice paths, and skew tableaux, PhD thesis, Brandeis Univ. Dep. Math. ProQuest, UMI Diss. Publ., 2013, 69 pp. | MR

[15] Feller W., An Introduction to Probability Theory and Its Applications, v. 1, 3rd edition, Wiley, 1968, 528 pp. ; Feller V., Vvedenie v teoriyu veroyatnostei i ee prilozheniya, V 2-kh tomakh. T. 1, Mir, Moskva, 1984, 528 pp. | MR | Zbl | MR

[16] Zhuk S.N., “Ob onlain-algoritmakh upakovki pryamougolnikov v neskolko polos”, Diskretnaya matematika, 19:4 (2007), 117–131 | DOI | MR | Zbl