Zobrazeno 1 - 10
of 590
pro vyhledávání: '"Schlosser, Michael"'
Autor:
Cohl, Howard, Schlosser, Michael
Ismail and Wilson derived a generating function for Askey--Wilson polynomials which is given by a product of $q$-Gauss (Heine) nonterminating basic hypergeometric functions. We provide a generalization of that generating function which contains an ex
Externí odkaz:
http://arxiv.org/abs/2411.03571
Autor:
Schlosser, Michael J., Zhou, Nian Hong
We prove specific biases in the number of occurrences of parts belonging to two different residue classes $a$ and $b$, modulo a fixed non-negative integer $m$, for the sets of unrestricted partitions, partitions into distinct parts, and overpartition
Externí odkaz:
http://arxiv.org/abs/2408.14365
Publikováno v:
J. Symbol. Comput. 127 (2025), 102352
In his work on the twenty vertex model, Di Francesco [Electron. J. Combin. 28(4) (2021), Paper No. 4.38] found a determinant formula for the number of configurations in a specific such model, and he conjectured a closed form product formula for the e
Externí odkaz:
http://arxiv.org/abs/2401.08481
We introduce a finite-bound extension of a partition equinumerosity result which was orignally proposed as a problem by Andrews and Deutsch in 2016, and given a generalized form in 2018 by Smoot and Yang. We also give a simple bijective proof, itself
Externí odkaz:
http://arxiv.org/abs/2312.09973
We provide elliptic extensions of elementary identities such as the sum of the first $n$ odd or even numbers, the geometric sum and the sum of the first $n$ cubes. Many such identities, and their $q$-analogues, are indefinite sums, and can be obtaine
Externí odkaz:
http://arxiv.org/abs/2310.20219
Autor:
Ram, Samrith, Schlosser, Michael J.
We discuss the problem posed by Bender, Coley, Robbins and Rumsey of enumerating the number of subspaces which have a given profile with respect to a linear operator over the finite field $\mathbb{F}_q$. We solve this problem in the case where the op
Externí odkaz:
http://arxiv.org/abs/2309.06401
Autor:
Schlosser, Michael J.
We present a multinomial theorem for elliptic commuting variables. This result extends the author's previously obtained elliptic binomial theorem to higher rank. Two essential ingredients are a simple elliptic star-triangle relation, ensuring the uni
Externí odkaz:
http://arxiv.org/abs/2307.12921
Autor:
Schlosser, Michael J., Zhou, Nian Hong
Motivated by recent work of George Andrews and Mircea Merca on the expansion of the quotient of the truncation of Euler's pentagonal number series by the complete series, we provide similar expansion results for averages involving truncations of sele
Externí odkaz:
http://arxiv.org/abs/2307.10821
Publikováno v:
In: Andres, B., Bernard, F., Cremers, D., Frintrop, S., Goldl\"ucke, B., Ihrke, I. (eds) Pattern Recognition. DAGM GCPR 2022. Lecture Notes in Computer Science, vol 13485. Springer, Cham
Object detection is one of the key tasks in many applications of computer vision. Deep Neural Networks (DNNs) are undoubtedly a well-suited approach for object detection. However, such DNNs need highly adapted hardware together with hardware-specific
Externí odkaz:
http://arxiv.org/abs/2304.11580
The identity by Chaundy and Bullard expresses $1$ as a sum of two truncated binomial series in one variable where the truncations depend on two different non-negative integers. We present basic and elliptic extensions of the Chaundy--Bullard identity
Externí odkaz:
http://arxiv.org/abs/2304.10003