The Gaussian coefficients and overpartitions
نویسندگان
چکیده
We show that the formalism of overpartitions gives a simple involution for the product definition of the Gaussian coefficients. In the formulation of our involution, an overline in the representation of an overpartition is endowed with a weight.
منابع مشابه
AN OVERPARTITION ANALOGUE OF THE q-BINOMIAL COEFFICIENTS
We define an overpartition analogue of Gaussian polynomials (also known as q-binomial coefficients) as a generating function for the number of overpartitions fitting inside the M ×N rectangle. We call these new polynomials over Gaussian polynomials or over q-binomial coefficients. We investigate basic properties and applications of over q-binomial coefficients. In particular, via the recurrence...
متن کاملn-COLOR OVERPARTITIONS, TWISTED DIVISOR FUNCTIONS, AND ROGERS-RAMANUJAN IDENTITIES
In the early 90’s Andrews discussed a certain q-series whose coefficients are determined by a twisted divisor function. We provide several other examples of this nature. All of these q-series can be interpreted combinatorially in terms of n-color overpartitions, as can some closely related series occurring in identities of the Rogers-Ramanujan type.
متن کاملA generalisation of a second partition theorem of Andrews to overpartitions
In 1968 and 1969, Andrews proved two partition theorems of the Rogers-Ramanujan type which generalise Schur’s celebrated partition identity (1926). Andrews’ two generalisations of Schur’s theorem went on to become two of the most influential results in the theory of partitions, finding applications in combinatorics, representation theory and quantum algebra. In a recent paper, the author genera...
متن کاملComplete convergence of moving-average processes under negative dependence sub-Gaussian assumptions
The complete convergence is investigated for moving-average processes of doubly infinite sequence of negative dependence sub-gaussian random variables with zero means, finite variances and absolutely summable coefficients. As a corollary, the rate of complete convergence is obtained under some suitable conditions on the coefficients.
متن کاملSpeech Enhancement using Laplacian Mixture Model under Signal Presence Uncertainty
In this paper an estimator for speech enhancement based on Laplacian Mixture Model has been proposed. The proposed method, estimates the complex DFT coefficients of clean speech from noisy speech using the MMSE estimator, when the clean speech DFT coefficients are supposed mixture of Laplacians and the DFT coefficients of noise are assumed zero-mean Gaussian distribution. Furthermore, the MMS...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
- Discrete Mathematics
دوره 305 شماره
صفحات -
تاریخ انتشار 2005