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Proving q-binomial identities

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#combinatorics #binomial-coefficients #q-analogs #q-series
289
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A general Combinatorics problem (Coefficients of the q factorial)

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#combinatorics #integer-partitions #q-analogs
695
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Which families of groups have interesting formulas for the number of elements of given order?

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#abstract-algebra #group-theory #elementary-number-theory #finite-groups #q-analogs
688
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How to prove it? (one of the Rogers-Ramanujan identities)

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#combinatorics #sequences-and-series #generating-functions #integer-partitions #q-analogs
185
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Recurrence formula of the MacMahon $q$-analog of the Catalan numbers

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#sequences-and-series #combinatorics #combinatorial-proofs #catalan-numbers #q-analogs
72
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Divisor Polynomials

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#number-theory #polynomials #q-analogs
174
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The $q$ Multilinear Theorem

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#combinatorics #noncommutative-algebra #multinomial-coefficients #multinomial-theorem #q-analogs
116
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Linear-algebraic interpretation of $q$-multichoose

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#combinatorics #binomial-coefficients #finite-fields #grassmannian #q-analogs
48
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Jacobi Quintuple Product Identity

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#combinatorics #quadratic-residues #theta-functions #q-analogs
50
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$q$-analog generalization for limits not going to 1

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#combinatorics #reference-request #generating-functions #q-analogs
51
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Discriminant of q-analogs of positive integers

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#reference-request #discriminant #q-analogs
334
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Combinatorial interpretation of $\frac{1}{1-e^{x+1}}$ or $\frac{1}{1-e^{x-1}}$

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#combinatorics #generating-functions #combinatorial-proofs #q-analogs #analytic-combinatorics
97
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On q-analogs of integer inequalities

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#algebra-precalculus #inequality #q-analogs
47
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A $\Bbb Z$-valued $\Bbb Q$-coefficient polynomial is a $\Bbb Z$-combination of $\binom{x}{k}$s: $q$-analog?

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#abstract-algebra #combinatorics #number-theory #binomial-coefficients #q-analogs
196
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What is the inverse of the $q$-exponential?

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#abstract-algebra #combinatorics #generating-functions #q-analogs

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