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An Area-to-Inv Bijection Between Dyck Paths and 312-avoiding Permutations
The symmetric $q,t$-Catalan polynomial $C_n(q,t)$, which specializes to the Catalan polynomial $C_n(q)$ when $t=1$, was defined by Garsia and Haiman in 1994. In 2000, Garsia and Haglund describedExpand
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EFFECTS OF CONCEPT-BASED INSTRUCTION ON STUDENTS' CONCEPTUAL UNDERSTANDING AND PROCEDURAL KNOWLEDGE OF CALCULUS
ABSTRACT An original study, involving 305 college-level calculus students and 8 instructors, and its replication study, conducted at the same university and involving 303 college-level calculusExpand
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A Schröder Generalization of Haglund's Statistic on Catalan Paths
Garsia and Haiman ( J. Algebraic. Combin. $\bf5$ $(1996)$, $191-244$) conjectured that a certain sum $C_n(q,t)$ of rational functions in $q,t$ reduces to a polynomial in $q,t$ with nonnegativeExpand
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Evacuation and a geometric construction for Fibonacci tableaux
Tableaux have long been used to study combinatorial properties of permutations and multiset permutations. Discovered independently by Robinson and Schensted and generalized by Knuth, theExpand
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Statistics on Linear Chord Diagrams
Linear chord diagrams are partitions of $\left[2n\right]$ into $n$ blocks of size two called chords. We refer to a block of the form $\{i,i+1\}$ as a short chord. In this paper, we study theExpand
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Wilf Equivalence for the Charge Statistic
Savage and Sagan have recently defined a notion of st-Wilf equivalence for any permutation statistic st and any two sets of permutations $\Pi$ and $\Pi'$. In this paper we give a thoroughExpand
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A Combinatorial Proof of a Recursion for the q-Kostka Polynomials
The Kostka numbers K?? play an important role in symmetric function theory, representation theory, combinatorics and invariant theory. The q-Kostka polynomials K??(q) are the q-analogues of theExpand
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Inversion polynomials for permutations avoiding consecutive patterns
In 2012, Sagan and Savage introduced the notion of $st$-Wilf equivalence for a statistic $st$ and for sets of permutations that avoid particular permutation patterns which can be extended toExpand
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A Weight-Preserving Bijection Between Schröder Paths and Schröder Permutations
Abstract. In 1993 Bonin, Shapiro, and Simion showed that the Schröder numbers count certain kinds of lattice paths; these paths are now called Schröder paths. In 1995 West showed that the SchröderExpand
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